diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html index b74f1c8..ce023c8 100644 --- a/src/axiom-website/CATS/index.html +++ b/src/axiom-website/CATS/index.html @@ -124,5 +124,39 @@ and reduced to a constant (usually 0). Schaums 14.646-14.677  source pdf
+ +
+This portion of the CATS suite involves Ordinary Differential Equations. +This is the Kamke test suite as published by + +E. S. Cheb-Terrab. They have been rewritten using Axiom syntax. +Where possible we show that the particular solution actually +satisfies the original ordinary differential equation.

+ + Kamke0 + source + pdf
+ Kamke1 + source + pdf
+ Kamke2 + source + pdf
+ Kamke3 + source + pdf
+ Kamke4 + source + pdf
+ Kamke5 + source + pdf
+ Kamke6 + source + pdf
+ Kamke7 + source + pdf
+ \ No newline at end of file diff --git a/src/axiom-website/CATS/kamke0.input.pamphlet b/src/axiom-website/CATS/kamke0.input.pamphlet new file mode 100644 index 0000000..d1a9d8b --- /dev/null +++ b/src/axiom-website/CATS/kamke0.input.pamphlet @@ -0,0 +1,1904 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input kamke0.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This is the first 50 of the Kamke test suite as published by +E. S. Cheb-Terrab\cite{1}. They have been rewritten using Axiom +syntax. Where possible we show that the particular solution actually +satisfies the original ordinary differential equation. +\end{abstract} +\eject +\tableofcontents +\eject +<<*>>= +)spool kamke0.output +)set break resume +)set mes auto off +)clear all + +--S 1 of 134 +y:=operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 1 + +--S 2 of 134 +f := operator 'f +--R +--R (2) f +--R Type: BasicOperator +--E 2 + +--S 3 of 134 +g := operator 'g +--R +--R (3) g +--R Type: BasicOperator +--E 3 + +--S 4 of 134 +ode1 := D(y(x),x) - (a4*x**4+a3*x**3+a2*x**2+a1*x+a0)**(-1/2) +--R +--R +--R +---------------------------------+ +--R | 4 3 2 , +--R \|a4 x + a3 x + a2 x + a1 x + a0 y (x) - 1 +--R +--R (4) --------------------------------------------- +--R +---------------------------------+ +--R | 4 3 2 +--R \|a4 x + a3 x + a2 x + a1 x + a0 +--R Type: Expression Integer +--E 4 + +--S 5 of 134 +ode1a:=solve(ode1,y,x) +--R +--R +--R (5) +--R x +--R ++ 1 +--I [particular= | ------------------------------------- d%N ,basis= ] +--R ++ +----------------------------------+ +--R | 4 3 2 +--I \|%N a4 + %N a3 + %N a2 + %N a1 + a0 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 5 + +--S 6 of 134 +ode2 := D(y(x),x) + a*y(x) - c*exp(b*x) +--R +--R +--R , b x +--R (6) y (x) - c %e + a y(x) +--R +--R Type: Expression Integer +--E 6 + +--S 7 of 134 +ode2a:=solve(ode2,y,x) +--R +--R +--R b x +--R c %e - a x +--R (7) [particular= -------,basis= [%e ]] +--R b + a +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 7 + +--S 8 of 134 +yx:=ode2a.particular +--R +--R b x +--R c %e +--R (8) ------- +--R b + a +--R Type: Expression Integer +--E 8 + +--S 9 of 134 +ode2expr:=D(yx,x) + a*yx -c*exp(b*x) +--R +--R (9) 0 +--R Type: Expression Integer +--E 9 + +--S 10 of 134 +ode3 := D(y(x),x) + a*y(x) - b*sin(c*x) +--R +--R , +--R (10) y (x) - b sin(c x) + a y(x) +--R +--R Type: Expression Integer +--E 10 + +--S 11 of 134 +ode3a:=solve(ode3,y,x) +--R +--R a b sin(c x) - b c cos(c x) - a x +--R (11) [particular= ---------------------------,basis= [%e ]] +--R 2 2 +--R c + a +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 11 + +--S 12 of 134 +yx:=ode3a.particular +--R +--R a b sin(c x) - b c cos(c x) +--R (12) --------------------------- +--R 2 2 +--R c + a +--R Type: Expression Integer +--E 12 + +--S 13 of 134 +ode3expr:=D(yx,x) + a*yx - b*sin(c*x) +--R +--R (13) 0 +--R Type: Expression Integer +--E 13 + +--S 14 of 134 +ode4 := D(y(x),x) + 2*x*y(x) - x*exp(-x**2) +--R +--R 2 +--R , - x +--R (14) y (x) - x %e + 2x y(x) +--R +--R Type: Expression Integer +--E 14 + +--S 15 of 134 +ode4a:=solve(ode4,y,x) +--R +--R 2 +--R 2 - x 2 +--R x %e - x +--R (15) [particular= --------,basis= [%e ]] +--R 2 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 15 + +--S 16 of 134 +yx:=ode4a.particular +--R +--R 2 +--R 2 - x +--R x %e +--R (16) -------- +--R 2 +--R Type: Expression Integer +--E 16 + +--S 17 of 134 +ode4expr:=D(yx,x) + 2*x*yx - x*exp(-x**2) +--R +--R (17) 0 +--R Type: Expression Integer +--E 17 + +--S 18 of 134 +ode5 := D(y(x),x) + y(x)*cos(x) - exp(2*x) +--R +--R , 2x +--R (18) y (x) - %e + y(x)cos(x) +--R +--R Type: Expression Integer +--E 18 + +--S 19 of 134 +ode5a:=solve(ode5,y,x) +--R +--I x 2%H +--R - sin(x) ++ %e - sin(x) +--I (19) [particular= %e | ----------- d%H ,basis= [%e ]] +--I ++ - sin(%H) +--R %e +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 19 + +--S 20 of 134 +ode6 := D(y(x),x) + y(x)*cos(x) - sin(2*x)/2 +--R +--R , +--R 2y (x) - sin(2x) + 2y(x)cos(x) +--R +--R (20) ------------------------------ +--R 2 +--R Type: Expression Integer +--E 20 + +--S 21 of 134 +ode6a:=solve(ode6,y,x) +--R +--R - sin(x) +--R (21) [particular= sin(x) - 1,basis= [%e ]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 21 + +--S 22 of 134 +yx:=ode6a.particular +--R +--R (22) sin(x) - 1 +--R Type: Expression Integer +--E 22 + +--S 23 of 134 +ode6expr:=D(yx,x) + yx*cos(x) - sin(2*x)/2 +--R +--R - sin(2x) + 2cos(x)sin(x) +--R (23) ------------------------- +--R 2 +--R Type: Expression Integer +--E 23 + +--S 24 of 134 +sin2rule := rule 2*cos(x)*sin(x) == sin(2*x) +--R +--I (24) 2%Y cos(x)sin(x) == %Y sin(2x) +--R Type: RewriteRule(Integer,Integer,Expression Integer) +--E 24 + +--S 25 of 134 +sin2rule ode6expr +--R +--R (25) 0 +--R Type: Expression Integer +--E 25 + +--S 26 of 134 +ode7 := D(y(x),x) + y(x)*cos(x) - exp(-sin(x)) +--R +--R , - sin(x) +--R (26) y (x) - %e + y(x)cos(x) +--R +--R Type: Expression Integer +--E 26 + +--S 27 of 134 +ode7a:=solve(ode7,y,x) +--R +--R - sin(x) - sin(x) +--R (27) [particular= x %e ,basis= [%e ]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 27 + +--S 28 of 134 +yx:=ode7a.particular +--R +--R - sin(x) +--R (28) x %e +--R Type: Expression Integer +--E 28 + +--S 29 of 134 +ode7expr := D(yx,x) + yx*cos(x) - exp(-sin(x)) +--R +--R (29) 0 +--R Type: Expression Integer +--E 29 + +--S 30 of 134 +ode8 := D(y(x),x) + y(x)*tan(x) - sin(2*x) +--R +--R , +--R (30) y (x) + y(x)tan(x) - sin(2x) +--R +--R Type: Expression Integer +--E 30 + +--S 31 of 134 +ode8a:=solve(ode8,y,x) +--R +--R (31) +--R +-------+ +--R 2 | 1 +--R (- 2cos(x) + 2cos(x)) |------- +--R 4| 4 +--R \|cos(x) 1 +--R [particular= --------------------------------,basis= [--------------]] +--R +-----------+ +-----------+ +--R | 2 | 2 +--R \|tan(x) + 1 \|tan(x) + 1 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 31 + +--S 32 of 134 +yx:=ode8a.particular +--R +--R +-------+ +--R 2 | 1 +--R (- 2cos(x) + 2cos(x)) |------- +--R 4| 4 +--R \|cos(x) +--R (32) -------------------------------- +--R +-----------+ +--R | 2 +--R \|tan(x) + 1 +--R Type: Expression Integer +--E 32 + +--S 33 of 134 +ode8expr:=D(yx,x) + yx*tan(x) - sin(2*x) +--R +--R +-------+3 +-----------+ +--R 3 | 1 | 2 +--R - cos(x) sin(2x) |------- \|tan(x) + 1 + 2sin(x) +--R 4| 4 +--R \|cos(x) +--R (33) --------------------------------------------------- +--R +-------+3 +-----------+ +--R 3 | 1 | 2 +--R cos(x) |------- \|tan(x) + 1 +--R 4| 4 +--R \|cos(x) +--R Type: Expression Integer +--E 33 + +--S 34 of 134 +ode9 := D(y(x),x) - (sin(log(x)) + cos(log(x)) +a)*y(x) +--R +--R , +--R (34) y (x) - y(x)sin(log(x)) - y(x)cos(log(x)) - a y(x) +--R +--R Type: Expression Integer +--E 34 + +--S 35 of 134 +ode9a:=solve(ode9,y,x) +--R +--R x sin(log(x)) + a x +--R (35) [particular= 0,basis= [%e ]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 35 + +--S 36 of 134 +yx:=ode9a.particular +--R +--R (36) 0 +--R Type: Expression Integer +--E 36 + +--S 37 of 134 +ode9expr:=D(yx,x) - (sin(log(x)) + cos(log(x)) +a)*yx +--R +--R (37) 0 +--R Type: Expression Integer +--E 37 + +--S 38 of 134 +ode10 := D(y(x),x) + D(f(x),x)*y(x) - f(x)*D(f(x),x) +--R +--R , , +--R (38) y (x) + (y(x) - f(x))f (x) +--R +--R Type: Expression Integer +--E 38 + +--S 39 of 134 +ode10a:=solve(ode10,y,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 39 + +--S 40 of 134 +ode11 := D(y(x),x) + f(x)*y(x) - g(x) +--R +--R , +--R (39) y (x) + f(x)y(x) - g(x) +--R +--R Type: Expression Integer +--E 40 + +--S 41 of 134 +ode11a:=solve(ode11,y,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 41 + +--S 42 of 134 +ode12 := D(y(x),x) + y(x)**2 - 1 +--R +--R , 2 +--R (40) y (x) + y(x) - 1 +--R +--R Type: Expression Integer +--E 42 + +--S 43 of 134 +yx:=solve(ode12,y,x) +--R +--R - log(y(x) + 1) + log(y(x) - 1) + 2x +--R (41) ------------------------------------ +--R 2 +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 134 +ode12expr:=D(yx,x) + yx**2 - 1 +--R +--R (42) +--R , 2 2 +--R 4y (x) + (y(x) - 1)log(y(x) + 1) +--R +--R + +--R 2 2 +--R ((- 2y(x) + 2)log(y(x) - 1) - 4x y(x) + 4x)log(y(x) + 1) +--R + +--R 2 2 2 2 2 2 +--R (y(x) - 1)log(y(x) - 1) + (4x y(x) - 4x)log(y(x) - 1) + 4x y(x) - 4x +--R / +--R 2 +--R 4y(x) - 4 +--R Type: Expression Integer +--E 44 + +--S 45 of 134 +ode13 := D(y(x),x) + y(x)**2 - a*x - b +--R +--R , 2 +--R (43) y (x) + y(x) - a x - b +--R +--R Type: Expression Integer +--E 45 + +--S 46 of 134 +ode13a:=solve(ode13,y,x) +--R +--R (44) "failed" +--R Type: Union("failed",...) +--E 46 + +--S 47 of 134 +ode14 := D(y(x),x) + y(x)**2 + a*x**m +--R +--R +--R , m 2 +--R (45) y (x) + a x + y(x) +--R +--R Type: Expression Integer +--E 47 + +--S 48 of 134 +ode14a:=solve(ode14,y,x) +--R +--R (46) "failed" +--R Type: Union("failed",...) +--E 48 + +--S 49 of 134 +ode15 := D(y(x),x) + y(x)**2 - 2*x**2*y(x) + x**4 -2*x-1 +--R +--R +--R , 2 2 4 +--R (47) y (x) + y(x) - 2x y(x) + x - 2x - 1 +--R +--R Type: Expression Integer +--E 49 + +--S 50 of 134 +yx:=solve(ode15,y,x) +--R +--R 2 +--R y(x) - x + 1 +--R (48) --------------------- +--R 2 2x +--R (2y(x) - 2x - 2)%e +--R Type: Union(Expression Integer,...) +--E 50 + +--S 51 of 134 +ode15expr:=D(yx,x) + yx**2 - 2*x**2*yx + x**4 -2*x-1 +--R +--R (49) +--R 2x , +--R - 4%e y (x) +--R +--R + +--R 4 2 6 4 3 2 8 +--R (4x - 8x - 4)y(x) + (- 8x - 8x + 16x + 8x + 16x + 8)y(x) + 4x +--R + +--R 6 5 3 2 +--R 8x - 8x - 16x - 8x - 8x - 4 +--R * +--R 2x 2 +--R (%e ) +--R + +--R 2 2 4 2 6 4 2 2x +--R ((- 4x - 4)y(x) + (8x + 8x )y(x) - 4x - 4x + 4x + 8x + 4)%e +--R + +--R 2 2 4 2 +--R y(x) + (- 2x + 2)y(x) + x - 2x + 1 +--R / +--R 2 2 4 2 2x 2 +--R (4y(x) + (- 8x - 8)y(x) + 4x + 8x + 4)(%e ) +--R Type: Expression Integer +--E 51 + +--S 52 of 134 +ode16 := D(y(x),x) + y(x)**2 +(x*y(x)-1)*f(x) +--R +--R , 2 +--R (50) y (x) + y(x) + x f(x)y(x) - f(x) +--R +--R Type: Expression Integer +--E 52 + +--S 53 of 134 +ode16a:=solve(ode16,y,x) +--R +--R (51) "failed" +--R Type: Union("failed",...) +--E 53 + +--S 54 of 134 +ode17 := D(y(x),x) - y(x)**2 -3*y(x) + 4 +--R +--R +--R , 2 +--R (52) y (x) - y(x) - 3y(x) + 4 +--R +--R Type: Expression Integer +--E 54 + +--S 55 of 134 +yx:=solve(ode17,y,x) +--R +--R +--R - log(y(x) + 4) + log(y(x) - 1) - 5x +--R (53) ------------------------------------ +--R 5 +--R Type: Union(Expression Integer,...) +--E 55 + +--S 56 of 134 +ode17expr:=D(yx,x) - yx**2 -3*yx + 4 +--R +--R (54) +--R , 2 2 +--R 25y (x) + (- y(x) - 3y(x) + 4)log(y(x) + 4) +--R +--R + +--R 2 2 +--R (2y(x) + 6y(x) - 8)log(y(x) - 1) + (- 10x + 15)y(x) +--R + +--R (- 30x + 45)y(x) + 40x - 60 +--R * +--R log(y(x) + 4) +--R + +--R 2 2 +--R (- y(x) - 3y(x) + 4)log(y(x) - 1) +--R + +--R 2 +--R ((10x - 15)y(x) + (30x - 45)y(x) - 40x + 60)log(y(x) - 1) +--R + +--R 2 2 2 2 +--R (- 25x + 75x + 75)y(x) + (- 75x + 225x + 225)y(x) + 100x - 300x - 300 +--R / +--R 2 +--R 25y(x) + 75y(x) - 100 +--R Type: Expression Integer +--E 56 + +--S 57 of 134 +ode18 := D(y(x),x) - y(x)**2 - x*y(x) - x + 1 +--R +--R +--R , 2 +--R (55) y (x) - y(x) - x y(x) - x + 1 +--R +--R Type: Expression Integer +--E 57 + +--S 58 of 134 +yx:=solve(ode18,y,x) +--R +--R +--R 2 +--R - x + 4x +--R --------- x +--R 2 ++ 1 +--I (- y(x) - 1)%e | - ------------- d%N + 1 +--R ++ 2 +--I - %N + 4%N +--R ----------- +--R 2 +--R %e +--R (56) ---------------------------------------------------- +--R 2 +--R - x + 4x +--R --------- +--R 2 +--R (y(x) + 1)%e +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 of 134 +ode18expr:=D(yx,x) - yx**2 - x*yx - x + 1 +--R (57) +--R 2 2 +--R - x + 4x +--R --------- x 2 +--R 2 2 ++ 1 +--I (- y(x) - 2y(x) - 1)(%e ) | - ------------- d%H +--R ++ 2 +--I - %H + 4%H +--R ----------- +--R 2 +--R %e +--R + +--R 2 2 2 +--R - x + 4x - x + 4x +--R --------- --------- +--R 2 2 2 +--R ((x y(x) + 2x y(x) + x)(%e ) + (2y(x) + 2)%e ) +--R * +--R x +--R ++ 1 +--I | - ------------- d%H +--R ++ 2 +--I - %H + 4%H +--R ----------- +--R 2 +--R %e +--R + +--R 2 +--R - x + 4x +--R --------- +--R 2 , +--R - %e y (x) +--R +--R + +--R 2 2 +--R - x + 4x +--R --------- +--R 2 2 +--R ((- x + 1)y(x) + (- 2x + 2)y(x) - x + 1)(%e ) +--R + +--R 2 +--R - x + 4x +--R --------- +--R 2 2 +--R (y(x) - 1)%e - 1 +--R / +--R 2 2 +--R - x + 4x +--R --------- +--R 2 2 +--R (y(x) + 2y(x) + 1)(%e ) +--R Type: Expression Integer +--E 59 + +--S 60 of 134 +ode19 := D(y(x),x) - (y(x) + x)**2 +--R +--R +--R , 2 2 +--R (58) y (x) - y(x) - 2x y(x) - x +--R +--R Type: Expression Integer +--E 60 + +--S 61 of 134 +yx:=solve(ode19,y,x) +--R +--R +--R +---+ +--R - y(x) + \|- 1 - x +--R (59) -------------------------------------- +--R +---+ +--R +---+ +---+ 2x\|- 1 +--R (2\|- 1 y(x) + 2x\|- 1 - 2)%e +--R Type: Union(Expression Integer,...) +--E 61 + +--S 62 of 134 +ode19expr := D(yx,x) - (yx + x)**2 +--R +--R (60) +--R +---+ +--R 2x\|- 1 , +--R - 4%e y (x) +--R +--R + +--R 2 2 2 +---+ 3 3 +---+ 4 2 +--R (- 4x y(x) + (- 8x \|- 1 - 8x )y(x) - 8x \|- 1 - 4x + 4x ) +--R * +--R +---+ 2 +--R 2x\|- 1 +--R (%e ) +--R + +--R +---+ 2 2 +---+ 3 +---+ +--R (- 4x\|- 1 + 4)y(x) + (- 8x \|- 1 + 8x)y(x) + (- 4x - 4x)\|- 1 +--R + +--R 2 +--R 4x +--R * +--R +---+ +--R 2x\|- 1 +--R %e +--R + +--R 2 +---+ +---+ 2 +--R y(x) + (- 2\|- 1 + 2x)y(x) - 2x\|- 1 + x - 1 +--R / +--R +---+ 2 +--R 2 +---+ +---+ 2 2x\|- 1 +--R (4y(x) + (8\|- 1 + 8x)y(x) + 8x\|- 1 + 4x - 4)(%e ) +--R Type: Expression Integer +--E 62 + +--S 63 of 134 +ode20 := D(y(x),x) - y(x)**2 +(x**2 + 1)*y(x) - 2*x +--R +--R +--R , 2 2 +--R (61) y (x) - y(x) + (x + 1)y(x) - 2x +--R +--R Type: Expression Integer +--E 63 + +--S 64 of 134 +yx:=solve(ode20,y,x) +--R +--R 3 +--R - x - 3x +--R --------- x +--R 2 3 ++ 1 +--I (- y(x) + x + 1)%e | - ------------- d%H + 1 +--R ++ 3 +--I - %H - 3%H +--R ----------- +--R 3 +--R %e +--R (62) --------------------------------------------------------- +--R 3 +--R - x - 3x +--R --------- +--R 2 3 +--R (y(x) - x - 1)%e +--R Type: Union(Expression Integer,...) +--E 64 + +--S 65 of 134 +ode20expr:=D(yx,x) - yx**2 +(x**2 + 1)*yx - 2*x +--R +--R (63) +--R 3 2 +--R - x - 3x +--R --------- +--R 2 2 4 2 3 +--R (- y(x) + (2x + 2)y(x) - x - 2x - 1)(%e ) +--R * +--R x 2 +--R ++ 1 +--I | - ------------- d%H +--R ++ 3 +--I - %H - 3%H +--R ----------- +--R 3 +--R %e +--R + +--R 2 2 4 2 6 4 2 +--R ((- x - 1)y(x) + (2x + 4x + 2)y(x) - x - 3x - 3x - 1) +--R * +--R 3 2 +--R - x - 3x +--R --------- +--R 3 +--R (%e ) +--R + +--R 3 +--R - x - 3x +--R --------- +--R 2 3 +--R (2y(x) - 2x - 2)%e +--R * +--R x +--R ++ 1 +--I | - ------------- d%H +--R ++ 3 +--I - %H - 3%H +--R ----------- +--R 3 +--R %e +--R + +--R 3 +--R - x - 3x +--R --------- +--R 3 , +--R - %e y (x) +--R +--R + +--R 3 2 +--R - x - 3x +--R --------- +--R 2 3 5 3 3 +--R (- 2x y(x) + (4x + 4x)y(x) - 2x - 4x - 2x)(%e ) +--R + +--R 3 +--R - x - 3x +--R --------- +--R 2 4 2 3 +--R (y(x) - x - 2x + 2x - 1)%e - 1 +--R / +--R 3 2 +--R - x - 3x +--R --------- +--R 2 2 4 2 3 +--R (y(x) + (- 2x - 2)y(x) + x + 2x + 1)(%e ) +--R Type: Expression Integer +--E 65 + +--S 66 of 134 +ode21 := D(y(x),x) - y(x)**2 +y(x)*sin(x) - cos(x) +--R +--R +--R , 2 +--R (64) y (x) + y(x)sin(x) - cos(x) - y(x) +--R +--R Type: Expression Integer +--E 66 + +--S 67 of 134 +ode21a:=solve(ode21,y,x) +--R +--R +--R (65) "failed" +--R Type: Union("failed",...) +--E 67 + +--S 68 of 134 +ode22 := D(y(x),x) - y(x)**2 -y(x)*sin(2*x) - cos(2*x) +--R +--R +--R , 2 +--R (66) y (x) - y(x)sin(2x) - cos(2x) - y(x) +--R +--R Type: Expression Integer +--E 68 + +--S 69 of 134 +ode22a:=solve(ode22,y,x) +--R +--R +--R (67) "failed" +--R Type: Union("failed",...) +--E 69 + +--S 70 of 134 +ode23 := D(y(x),x) + a*y(x)**2 - b +--R +--R +--R , 2 +--R (68) y (x) + a y(x) - b +--R +--R Type: Expression Integer +--E 70 + +--S 71 of 134 +yx:=solve(ode23,y,x) +--R +--R +--R 2 +---+ +--R (a y(x) + b)\|a b - 2a b y(x) +---+ +--R log(-------------------------------) + 2x\|a b +--R 2 +--R a y(x) - b +--R (69) ----------------------------------------------- +--R +---+ +--R 2\|a b +--R Type: Union(Expression Integer,...) +--E 71 + +--S 72 of 134 +ode23expr := D(yx,x) + a*yx**2 - b +--R +--R (70) +--R 2 +---+ 2 +--R , 2 (a y(x) + b)\|a b - 2a b y(x) +--R 4by (x) + (a y(x) - b)log(-------------------------------) +--R 2 +--R a y(x) - b +--R + +--R 2 +---+ +--R 2 +---+ (a y(x) + b)\|a b - 2a b y(x) +--R (4a x y(x) - 4b x)\|a b log(-------------------------------) +--R 2 +--R a y(x) - b +--R + +--R 2 2 2 2 2 2 3 2 +--R (4a b x - 4a b + 4a b)y(x) - 4a b x + 4b - 4b +--R / +--R 2 2 +--R 4a b y(x) - 4b +--R Type: Expression Integer +--E 72 + +--S 73 of 134 +ode24 := D(y(x),x) + a*y(x)**2 - b*x**nu +--R +--R +--R , nu 2 +--R (71) y (x) - b x + a y(x) +--R +--R Type: Expression Integer +--E 73 + +--S 74 of 134 +ode24a:=solve(ode24,y,x) +--R +--R +--R (72) "failed" +--R Type: Union("failed",...) +--E 74 + +--S 75 of 134 +ode25 := D(y(x),x) + a*y(x)**2 - b*x**(2*nu) - c*x**(nu-1) +--R +--R +--R , 2nu nu - 1 2 +--R (73) y (x) - b x - c x + a y(x) +--R +--R Type: Expression Integer +--E 75 + +--S 76 of 134 +ode25expr:=solve(ode25,y,x) +--R +--R +--R (74) "failed" +--R Type: Union("failed",...) +--E 76 + +--S 77 of 134 +ode26 := D(y(x),x) - (A*y(x) - a)*(B*y(x) - b) +--R +--R +--R , 2 +--R (75) y (x) - A B y(x) + (A b + B a)y(x) - a b +--R +--R Type: Expression Integer +--E 77 + +--S 78 of 134 +yx:=solve(ode26,y,x) +--R +--R +--R log(B y(x) - b) - log(A y(x) - a) + (- A b + B a)x +--R (76) -------------------------------------------------- +--R A b - B a +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 of 134 +ode26expr := D(yx,x) - (A*yx - a)*(B*yx - b) +--R +--R (77) +--R 2 2 2 2 , +--R (A b - 2A B a b + B a )y (x) +--R +--R + +--R 2 2 2 2 2 2 +--R (- A B y(x) + (A B b + A B a)y(x) - A B a b)log(B y(x) - b) +--R + +--R 2 2 2 2 2 +--R (2A B y(x) + (- 2A B b - 2A B a)y(x) + 2A B a b)log(A y(x) - a) +--R + +--R 3 2 2 3 3 2 3 2 2 +--R ((2A B b - 2A B a)x + A B b - A B a )y(x) +--R + +--R 3 2 3 2 3 3 2 2 2 2 3 3 +--R ((- 2A B b + 2A B a )x - A b - A B a b + A B a b + B a )y(x) +--R + +--R 2 2 2 2 2 3 2 3 +--R (2A B a b - 2A B a b)x + A a b - B a b +--R * +--R log(B y(x) - b) +--R + +--R 2 2 2 2 2 2 +--R (- A B y(x) + (A B b + A B a)y(x) - A B a b)log(A y(x) - a) +--R + +--R 3 2 2 3 3 2 3 2 2 +--R ((- 2A B b + 2A B a)x - A B b + A B a )y(x) +--R + +--R 3 2 3 2 3 3 2 2 2 2 3 3 +--R ((2A B b - 2A B a )x + A b + A B a b - A B a b - B a )y(x) +--R + +--R 2 2 2 2 2 3 2 3 +--R (- 2A B a b + 2A B a b)x - A a b + B a b +--R * +--R log(A y(x) - a) +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (- A B b + 2A B a b - A B a )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 3 3 +--R (- A B b + A B a b + A B a b - A B a )x - A B a b +--R + +--R 2 2 2 3 2 3 3 2 2 3 2 +--R (2A B a - A B)b + (- A B a + 2A B a)b - A B a +--R * +--R 2 +--R y(x) +--R + +--R 4 3 3 2 2 2 3 2 4 3 2 4 4 2 2 2 2 4 4 +--R (A B b - A B a b - A B a b + A B a )x + (A b - 2A B a b + B a )x +--R + +--R 3 4 2 2 3 3 2 3 2 2 3 4 2 2 +--R A a b + (- A B a + A )b + (- A B a - A B a)b + (B a - A B a )b +--R + +--R 3 3 +--R B a +--R * +--R y(x) +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- A B a b + 2A B a b - A B a b)x +--R + +--R 3 4 2 2 3 2 3 2 3 4 2 2 4 3 2 3 +--R (- A a b + A B a b + A B a b - B a b)x - A a b + (2A B a - A a)b +--R + +--R 2 4 2 2 2 3 +--R (- B a + 2A B a )b - B a b +--R / +--R 3 2 2 2 3 2 2 +--R (A B b - 2A B a b + A B a )y(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 2 2 2 3 +--R (- A b + A B a b + A B a b - B a )y(x) + A a b - 2A B a b + B a b +--R Type: Expression Integer +--E 79 + +--S 80 of 134 +ode27 := D(y(x),x) + a*y(x)*(y(x)-x) - 1 +--R +--R +--R , 2 +--R (78) y (x) + a y(x) - a x y(x) - 1 +--R +--R Type: Expression Integer +--E 80 + +--S 81 of 134 +ode27a:=solve(ode27,y,x) +--R +--R +--R 2 +--R a x +--R ---- x +--R 2 ++ a +--I (- y(x) + x)%e | ------ d%N + 1 +--R ++ 2 +--I %N a +--R ---- +--R 2 +--R %e +--R (79) -------------------------------------- +--R 2 +--R a x +--R ---- +--R 2 +--R (y(x) - x)%e +--R Type: Union(Expression Integer,...) +--E 81 + +--S 82 of 134 +ode28 := D(y(x),x) + x*y(x)**2 -x**3*y(x) - 2*x +--R +--R +--R , 2 3 +--R (80) y (x) + x y(x) - x y(x) - 2x +--R +--R Type: Expression Integer +--E 82 + +--S 83 of 134 +ode28a:=solve(ode28,y,x) +--R +--R +--R 4 +--R x +--R -- x +--I 2 4 ++ %N +--I (- y(x) + x )%e | ----- d%N + 1 +--R ++ 4 +--I %N +--R --- +--R 4 +--R %e +--R (81) ------------------------------------ +--R 4 +--R x +--R -- +--R 2 4 +--R (y(x) - x )%e +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 of 134 +ode29 := D(y(x),x) - x*y(x)**2 - 3*x*y(x) +--R +--R +--R , 2 +--R (82) y (x) - x y(x) - 3x y(x) +--R +--R Type: Expression Integer +--E 84 + +--S 85 of 134 +yx:=solve(ode29,y,x) +--R +--R +--R 2 +--R - 2log(y(x) + 3) + 2log(y(x)) - 3x +--R (83) ----------------------------------- +--R 6 +--R Type: Union(Expression Integer,...) +--E 85 + +--S 86 of 134 +ode29expr := D(yx,x) - x*yx**2 - 3*x*yx +--R +--R (84) +--R , 2 2 +--R 36y (x) + (- 4x y(x) - 12x y(x))log(y(x) + 3) +--R +--R + +--R 2 3 2 +--R (8x y(x) + 24x y(x))log(y(x)) + (- 12x + 36x)y(x) +--R + +--R 3 +--R (- 36x + 108x)y(x) +--R * +--R log(y(x) + 3) +--R + +--R 2 2 +--R (- 4x y(x) - 12x y(x))log(y(x)) +--R + +--R 3 2 3 +--R ((12x - 36x)y(x) + (36x - 108x)y(x))log(y(x)) +--R + +--R 5 3 2 5 3 +--R (- 9x + 54x - 36x)y(x) + (- 27x + 162x - 108x)y(x) +--R / +--R 2 +--R 36y(x) + 108y(x) +--R Type: Expression Integer +--E 86 + +--S 87 of 134 +ode30 := D(y(x),x) + x**(-a-1)*y(x)**2 - x**a +--R +--R +--R , a 2 - a - 1 +--R (85) y (x) - x + y(x) x +--R +--R Type: Expression Integer +--E 87 + +--S 88 of 134 +ode30a:=solve(ode30,y,x) +--R +--R +--R (86) "failed" +--R Type: Union("failed",...) +--E 88 + +--S 89 of 134 +ode31 := D(y(x),x) - a*x**n*(y(x)**2+1) +--R +--R +--R , 2 n +--R (87) y (x) + (- a y(x) - a)x +--R +--R Type: Expression Integer +--E 89 + +--S 90 of 134 +yx:=solve(ode31,y,x) +--R +--R +--R n log(x) +--R - a x %e + (n + 1)atan(y(x)) +--R (88) ------------------------------------ +--R n + 1 +--R Type: Union(Expression Integer,...) +--E 90 + +--S 91 of 134 +ode31expr := D(yx,x) - a*x**n*(yx**2+1) +--R +--R (89) +--R 2 , 3 2 2 3 2 n n log(x) 2 +--R (n + 2n + 1)y (x) + (- a x y(x) - a x )x (%e ) +--R +--R + +--R 2 2 2 2 2 n +--R ((2a n + 2a )x y(x) + (2a n + 2a )x)x atan(y(x)) +--R + +--R 2 2 2 +--R (- a n - 2a n - a)y(x) - a n - 2a n - a +--R * +--R n log(x) +--R %e +--R + +--R 2 2 2 n 2 +--R ((- a n - 2a n - a)y(x) - a n - 2a n - a)x atan(y(x)) +--R + +--R 2 2 2 n +--R ((- a n - 2a n - a)y(x) - a n - 2a n - a)x +--R / +--R 2 2 2 +--R (n + 2n + 1)y(x) + n + 2n + 1 +--R Type: Expression Integer +--E 91 + +--S 92 of 134 +ode32 := D(y(x),x) + y(x)**2*sin(x) - 2*sin(x)/cos(x)**2 +--R +--R +--R 2 , 2 2 +--R cos(x) y (x) + (y(x) cos(x) - 2)sin(x) +--R +--R (90) --------------------------------------- +--R 2 +--R cos(x) +--R Type: Expression Integer +--E 92 + +--S 93 of 134 +yx:=solve(ode32,y,x) +--R +--R +--R (91) "failed" +--R Type: Union("failed",...) +--E 93 + +--S 94 of 134 +ode33 := D(y(x),x) - y(x)**2*D(f(x),x)/g(x) + D(g(x),x)/f(x) +--R +--R , , 2 , +--R f(x)g(x)y (x) + g(x)g (x) - f(x)y(x) f (x) +--R +--R (92) ------------------------------------------ +--R f(x)g(x) +--R Type: Expression Integer +--E 94 + +--S 95 of 134 +ode33a:=solve(ode33,y,x) +--R +--R (93) "failed" +--R Type: Union("failed",...) +--E 95 + +--S 96 of 134 +ode34 := D(y(x),x) + f(x)*y(x)**2 + g(x)*y(x) +--R +--R , 2 +--R (94) y (x) + f(x)y(x) + g(x)y(x) +--R +--R Type: Expression Integer +--E 96 + +--S 97 of 134 +ode34a:=solve(ode34,y,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 97 + +--S 98 of 134 +ode35 := D(y(x),x) + f(x)*(y(x)**2 + 2*a*y(x) +b) +--R +--R , 2 +--R (95) y (x) + f(x)y(x) + 2a f(x)y(x) + b f(x) +--R +--R Type: Expression Integer +--E 98 + +--S 99 of 134 +yx:=solve(ode35,y,x) +--R +--R (96) +--R +--------+ x +--R | 2 ++ +--I 2\|- b + a | f(%H)d%H +--R ++ +--R + +--R +--------+ +--R 2 2 | 2 2 3 +--R (y(x) + 2a y(x) - b + 2a )\|- b + a + (2b - 2a )y(x) + 2a b - 2a +--R log(--------------------------------------------------------------------) +--R 2 +--R y(x) + 2a y(x) + b +--R / +--R +--------+ +--R | 2 +--R 2\|- b + a +--R Type: Union(Expression Integer,...) +--E 99 + +--S 100 of 134 +ode35expr := D(yx,x) + f(x)*(yx**2 + 2*a*yx +b) +--R +--R (97) +--R 2 2 3 2 2 +--R ((4b - 4a )f(x)y(x) + (8a b - 8a )f(x)y(x) + (4b - 4a b)f(x)) +--R * +--R +--------+ x 2 +--R | 2 ++ +--I \|- b + a | f(%H)d%H +--R ++ +--R + +--R 2 2 3 2 2 +--R ((4b - 4a )f(x)y(x) + (8a b - 8a )f(x)y(x) + (4b - 4a b)f(x)) +--R * +--R log +--R +--------+ +--R 2 2 | 2 2 +--R (y(x) + 2a y(x) - b + 2a )\|- b + a + (2b - 2a )y(x) +--R + +--R 3 +--R 2a b - 2a +--R / +--R 2 +--R y(x) + 2a y(x) + b +--R + +--R 3 2 2 4 +--R (8a b - 8a )f(x)y(x) + (16a b - 16a )f(x)y(x) +--R + +--R 2 3 +--R (8a b - 8a b)f(x) +--R * +--R +--------+ +--R | 2 +--R \|- b + a +--R * +--R x +--R ++ +--I | f(%H)d%H +--R ++ +--R + +--R +--------+ +--R 2 | 2 , +--R (4b - 4a )\|- b + a y (x) +--R +--R + +--R +--------+ +--R 2 | 2 +--R (- f(x)y(x) - 2a f(x)y(x) - b f(x))\|- b + a +--R * +--R log +--R +--------+ +--R 2 2 | 2 2 +--R (y(x) + 2a y(x) - b + 2a )\|- b + a + (2b - 2a )y(x) + 2a b +--R + +--R 3 +--R - 2a +--R / +--R 2 +--R y(x) + 2a y(x) + b +--R ** +--R 2 +--R + +--R 3 2 2 4 2 3 +--R ((4a b - 4a )f(x)y(x) + (8a b - 8a )f(x)y(x) + (4a b - 4a b)f(x)) +--R * +--R +--------+ +--R 2 2 | 2 2 3 +--R (y(x) + 2a y(x) - b + 2a )\|- b + a + (2b - 2a )y(x) + 2a b - 2a +--R log(--------------------------------------------------------------------) +--R 2 +--R y(x) + 2a y(x) + b +--R + +--R 2 2 2 2 +--R (4b + (- 4a + 4)b - 4a )f(x)y(x) +--R + +--R 2 3 3 +--R (8a b + (- 8a + 8a)b - 8a )f(x)y(x) +--R + +--R 3 2 2 2 +--R (4b + (- 4a + 4)b - 4a b)f(x) +--R * +--R +--------+ +--R | 2 +--R \|- b + a +--R / +--R +--------+ +--R 2 2 3 2 2 | 2 +--R ((4b - 4a )y(x) + (8a b - 8a )y(x) + 4b - 4a b)\|- b + a +--R Type: Expression Integer +--E 100 + +--S 101 of 134 +ode36 := D(y(x),x) + y(x)**3 + a*x*y(x)**2 +--R +--R +--R , 3 2 +--R (98) y (x) + y(x) + a x y(x) +--R +--R Type: Expression Integer +--E 101 + +--S 102 of 134 +ode36a:=solve(ode36,y,x) +--R +--R +--R (99) "failed" +--R Type: Union("failed",...) +--E 102 + +--S 103 of 134 +ode37 := D(y(x),x) - y(x)**3 - a*exp(x)*y(x)**2 +--R +--R , 2 x 3 +--R (100) y (x) - a y(x) %e - y(x) +--R +--R Type: Expression Integer +--E 103 + +--S 104 of 134 +ode37a:=solve(ode37,y,x) +--R +--R (101) "failed" +--R Type: Union("failed",...) +--E 104 + +--S 105 of 134 +ode38 := D(y(x),x) - a*y(x)**3 - b*x**(3/2) +--R +--R , +-+ 3 +--R (102) y (x) - b x\|x - a y(x) +--R +--R Type: Expression Integer +--E 105 + +--S 106 of 134 +ode38a:=solve(ode38,y,x) +--R +--R (103) "failed" +--R Type: Union("failed",...) +--E 106 + +--S 107 of 134 +ode39 := D(y(x),x) - a3*y(x)**3 - a2*y(x)**2 - a1*y(x) - a0 +--R +--R , 3 2 +--R (104) y (x) - a3 y(x) - a2 y(x) - a1 y(x) - a0 +--R +--R Type: Expression Integer +--E 107 + +--S 108 of 134 +yx:=solve(ode39,y,x) +--R +--R +--R (105) +--R ROOT +--R 2 2 3 3 2 2 +--R (- 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2 + 3a1 a2 ) +--R * +--R 2 +--I %%CK0 +--R + +--R 2 +--R 12a1 a3 - 4a2 +--R / +--R 2 2 3 3 2 2 +--R 27a0 a3 + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2 - a1 a2 +--R + +--I - %%CK0 +--R * +--R log +--R 2 3 2 2 2 4 2 +--R 162a0 a1 a3 + (- 54a0 a2 - 108a0 a1 a2 + 24a1 )a3 +--R + +--R 3 3 2 5 2 4 +--R (60a0 a1 a2 - 14a1 a2 )a3 - 8a0 a2 + 2a1 a2 +--R * +--I %%CK0 +--R + +--R 2 3 3 2 3 2 2 +--R 81a0 a3 + (- 54a0 a1 a2 + 12a1 )a3 + (12a0 a2 - 3a1 a2 )a3 +--R * +--R ROOT +--R 2 2 3 3 +--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2 +--R + +--R 2 2 +--R 3a1 a2 +--R * +--R 2 +--I %%CK0 +--R + +--R 2 +--R 12a1 a3 - 4a2 +--R / +--R 2 2 3 3 2 2 +--R 27a0 a3 + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2 - a1 a2 +--R + +--R 2 3 2 2 2 4 2 +--R 162a0 a1 a3 + (- 54a0 a2 - 108a0 a1 a2 + 24a1 )a3 +--R + +--R 3 3 2 5 2 4 +--R (60a0 a1 a2 - 14a1 a2 )a3 - 8a0 a2 + 2a1 a2 +--R * +--R 2 +--I %%CK0 +--R + +--R 2 3 3 2 +--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 +--R + +--R 3 2 2 +--R (- 12a0 a2 + 3a1 a2 )a3 +--R * +--I %%CK0 +--R + +--R 3 2 3 2 2 +--R (54a0 a3 - 18a1 a2 a3 + 4a2 a3)y(x) + (18a0 a2 - 12a1 )a3 +--R + +--R 2 +--R 2a1 a2 a3 +--R + +--R - +--R ROOT +--R 2 2 3 3 +--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2 +--R + +--R 2 2 +--R 3a1 a2 +--R * +--R 2 +--I %%CK0 +--R + +--R 2 +--R 12a1 a3 - 4a2 +--R / +--R 2 2 3 3 2 2 +--R 27a0 a3 + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2 - a1 a2 +--R + +--I - %%CK0 +--R * +--R log +--R 2 3 2 2 2 4 2 +--R - 162a0 a1 a3 + (54a0 a2 + 108a0 a1 a2 - 24a1 )a3 +--R + +--R 3 3 2 5 2 4 +--R (- 60a0 a1 a2 + 14a1 a2 )a3 + 8a0 a2 - 2a1 a2 +--R * +--I %%CK0 +--R + +--R 2 3 3 2 3 2 2 +--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 + (- 12a0 a2 + 3a1 a2 )a3 +--R * +--R ROOT +--R 2 2 3 3 +--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2 +--R + +--R 2 2 +--R 3a1 a2 +--R * +--R 2 +--I %%CK0 +--R + +--R 2 +--R 12a1 a3 - 4a2 +--R / +--R 2 2 3 3 2 2 +--R 27a0 a3 + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2 - a1 a2 +--R + +--R 2 3 2 2 2 4 2 +--R 162a0 a1 a3 + (- 54a0 a2 - 108a0 a1 a2 + 24a1 )a3 +--R + +--R 3 3 2 5 2 4 +--R (60a0 a1 a2 - 14a1 a2 )a3 - 8a0 a2 + 2a1 a2 +--R * +--R 2 +--I %%CK0 +--R + +--R 2 3 3 2 +--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 +--R + +--R 3 2 2 +--R (- 12a0 a2 + 3a1 a2 )a3 +--R * +--I %%CK0 +--R + +--R 3 2 3 2 2 +--R (54a0 a3 - 18a1 a2 a3 + 4a2 a3)y(x) + (18a0 a2 - 12a1 )a3 +--R + +--R 2 +--R 2a1 a2 a3 +--R + +--I 2%%CK0 +--R * +--R log +--R 2 3 2 2 2 4 2 +--R - 162a0 a1 a3 + (54a0 a2 + 108a0 a1 a2 - 24a1 )a3 +--R + +--R 3 3 2 5 2 4 +--R (- 60a0 a1 a2 + 14a1 a2 )a3 + 8a0 a2 - 2a1 a2 +--R * +--R 2 +--I %%CK0 +--R + +--R 2 3 3 2 3 2 2 +--R (81a0 a3 + (- 54a0 a1 a2 + 12a1 )a3 + (12a0 a2 - 3a1 a2 )a3) +--R * +--I %%CK0 +--R + +--R 3 2 3 2 2 +--R (27a0 a3 - 9a1 a2 a3 + 2a2 a3)y(x) + (9a0 a2 + 12a1 )a3 +--R + +--R 2 4 +--R - 11a1 a2 a3 + 2a2 +--R + +--R - 2x +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 108 + +--S 109 of 134 +ode40 := D(y(x),x) + 3*a*y(x)**3 + 6*a*x*y(x)**2 +--R +--R , 3 2 +--R (106) y (x) + 3a y(x) + 6a x y(x) +--R +--R Type: Expression Integer +--E 109 + +--S 110 of 134 +ode40a:=solve(ode40,y,x) +--R +--R (107) "failed" +--R Type: Union("failed",...) +--E 110 + +--S 111 of 134 +ode41 := D(y(x),x) + a*x*y(x)**3 + b*y(x)**2 +--R +--R , 3 2 +--R (108) y (x) + a x y(x) + b y(x) +--R +--R Type: Expression Integer +--E 111 + +--S 112 of 134 +ode41a:=solve(ode41,y,x) +--R +--R (109) "failed" +--R Type: Union("failed",...) +--E 112 + +--S 113 of 134 +ode42 := D(y(x),x) - x*(x+2)*y(x)**3 - (x+3)*y(x)**2 +--R +--R , 2 3 2 +--R (110) y (x) + (- x - 2x)y(x) + (- x - 3)y(x) +--R +--R Type: Expression Integer +--E 113 + +--S 114 of 134 +ode42a:=solve(ode42,y,x) +--R +--R (111) "failed" +--R Type: Union("failed",...) +--E 114 + +--S 115 of 134 +ode43 := D(y(x),x) + (3*a*x**2 + 4*a**2*x + b)*y(x)**3 + 3*x*y(x)**2 +--R +--R , 2 2 3 2 +--R (112) y (x) + (3a x + 4a x + b)y(x) + 3x y(x) +--R +--R Type: Expression Integer +--E 115 + +--S 116 of 134 +ode43a:=solve(ode43,y,x) +--R +--R (113) "failed" +--R Type: Union("failed",...) +--E 116 + +--S 117 of 134 +ode44 := D(y(x),x) + 2*a*x**3*y(x)**3 + 2*x*y(x) +--R +--R , 3 3 +--R (114) y (x) + 2a x y(x) + 2x y(x) +--R +--R Type: Expression Integer +--E 117 + +--S 118 of 134 +yx:=solve(ode44,y,x) +--R +--R 2 2 +--R (2a x + a)y(x) + 2 +--R (115) -------------------- +--R 2 +--R 2 2x +--R 2y(x) %e +--R Type: Union(Expression Integer,...) +--E 118 + +--S 119 of 134 +ode44expr := D(yx,x) + 2*a*x**3*yx**3 + 2*x*yx +--R +--R (116) +--R 2 2 2 2 +--R 3 2x , 3 6 4 2x +--R - 8y(x) (%e ) y (x) + ((- 8a x + 4a x)y(x) - 8x y(x) )(%e ) +--R +--R + +--R 4 9 4 7 4 5 4 3 6 3 7 3 5 3 3 4 +--R (8a x + 12a x + 6a x + a x )y(x) + (24a x + 24a x + 6a x )y(x) +--R + +--R 2 5 2 3 2 3 +--R (24a x + 12a x )y(x) + 8a x +--R / +--R 2 3 +--R 6 2x +--R 4y(x) (%e ) +--R Type: Expression Integer +--E 119 + +--S 120 of 134 +ode45 := D(y(x),x) + 2*(a**2*x**3 - b**2*x)*y(x)**3 + 3*b*y(x)**2 +--R +--R , 2 3 2 3 2 +--R (117) y (x) + (2a x - 2b x)y(x) + 3b y(x) +--R +--R Type: Expression Integer +--E 120 + +--S 121 of 134 +ode45a:=solve(ode45,y,x) +--R +--R (118) "failed" +--R Type: Union("failed",...) +--E 121 + +--S 122 of 134 +ode46 := D(y(x),x) - x**a*y(x)**3 + 3*y(x)**2 - x**(-a)*y(x) _ + -x**(-2*a) + a*x**(-a-1) +--R +--R , 3 a - a - a - 1 - 2a 2 +--R (119) y (x) - y(x) x - y(x)x + a x - x + 3y(x) +--R +--R Type: Expression Integer +--E 122 + +--S 123 of 134 +ode46a:=solve(ode46,y,x) +--R +--R (120) "failed" +--R Type: Union("failed",...) +--E 123 + +--S 124 of 134 +ode47 := D(y(x),x) - a*(x**n - x)*y(x)**3 - y(x)**2 +--R +--R , 3 n 3 2 +--R (121) y (x) - a y(x) x + a x y(x) - y(x) +--R +--R Type: Expression Integer +--E 124 + +--S 125 of 134 +ode47a:=solve(ode47,y,x) +--R +--R (122) "failed" +--R Type: Union("failed",...) +--E 125 + +--S 126 of 134 +ode48 := D(y(x),x) - (a*x**n + b*x)*y(x)**3 - c*y(x)**2 +--R +--R , 3 n 3 2 +--R (123) y (x) - a y(x) x - b x y(x) - c y(x) +--R +--R Type: Expression Integer +--E 126 + +--S 127 of 134 +ode48a:=solve(ode48,y,x) +--R +--R (124) "failed" +--R Type: Union("failed",...) +--E 127 + +--S 128 of 134 +ode49 := D(y(x),x) + a*diff(phi(x),x)*y(x)**3 + 6*a*phi(x)*y(x)**2 + _ + (2*a+1)*y(x)*diff(phi(x),x,x)/diff(phi(x),x) +2*(a+1) +--R +--R There are no library operations named phi +--R Use HyperDoc Browse or issue +--R )what op phi +--R to learn if there is any operation containing " phi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named phi +--R with argument type(s) +--R Variable x +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 128 + +--S 129 of 134 +f1 := operator 'f1 +--R +--R (125) f1 +--R Type: BasicOperator +--E 129 + +--S 130 of 134 +f2 := operator 'f2 +--R +--R (126) f2 +--R Type: BasicOperator +--E 130 + +--S 131 of 134 +f3 := operator 'f3 +--R +--R (127) f3 +--R Type: BasicOperator +--E 131 + +--S 132 of 134 +f0 := operator 'f0 +--R +--R (128) f0 +--R Type: BasicOperator +--E 132 + +--S 133 of 134 +ode50 := D(y(x),x) - f3(x)*y(x)**3 - f2(x)*y(x)**2 - f1(x)*y(x) - f0(x) +--R +--R , 3 2 +--R (129) y (x) - f3(x)y(x) - f2(x)y(x) - f1(x)y(x) - f0(x) +--R +--R Type: Expression Integer +--E 133 + +--S 134 of 134 +ode50a:=solve(ode50,y,x) +--R +--R (130) "failed" +--R Type: Union("failed",...) +--E 134 + +)spool +)lisp (bye) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} {\bf http://www.cs.uwaterloo.ca/$\tilde{}$ecterrab/odetools.html} +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/kamke0.input.pdf b/src/axiom-website/CATS/kamke0.input.pdf new file mode 100644 index 0000000..fab2930 Binary files /dev/null and b/src/axiom-website/CATS/kamke0.input.pdf differ diff --git a/src/axiom-website/CATS/kamke1.input.pamphlet b/src/axiom-website/CATS/kamke1.input.pamphlet new file mode 100644 index 0000000..c60b4e0 --- /dev/null +++ b/src/axiom-website/CATS/kamke1.input.pamphlet @@ -0,0 +1,2060 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input kamke1.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This is the next 50 of the Kamke test suite as published by +E. S. Cheb-Terrab\cite{1}. They have been rewritten using Axiom +syntax. Where possible we show that the particular solution actually +satisfies the original ordinary differential equation. +\end{abstract} +\eject +\tableofcontents +\eject +<<*>>= +)spool kamke1.output +)set break resume +)set mes auto off +)clear all + +--S 1 of 120 +y:=operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 1 + +--S 2 of 120 +f := operator 'f +--R +--R (2) f +--R Type: BasicOperator +--E 2 + +--S 3 of 120 +g := operator 'g +--R +--R (3) g +--R Type: BasicOperator +--E 3 + +--S 4 of 120 +h := operator 'h +--R +--R (4) h +--R Type: BasicOperator +--E 4 + +--S 5 of 120 +ode51 := D(y(x),x) - (y(x)-f(x))*(y(x)-g(x))*(y(x)-(a*f(x)+b*g(x))/(a+b))*h(x)_ + - D(f(x),x)*(y(x)-g(x))/(f(x)-g(x)) _ + - D(g(x),x)*(y(x)-f(x))/(g(x)-f(x)) +--R +--R (5) +--R , , +--R ((b + a)g(x) + (- b - a)f(x))y (x) + ((- b - a)y(x) + (b + a)f(x))g (x) +--R +--R + +--R , +--R ((b + a)y(x) + (- b - a)g(x))f (x) +--R +--R + +--R 3 +--R ((- b - a)g(x) + (b + a)f(x))h(x)y(x) +--R + +--R 2 2 2 +--R ((2b + a)g(x) + (- b + a)f(x)g(x) + (- b - 2a)f(x) )h(x)y(x) +--R + +--R 3 2 2 3 +--R (- b g(x) + (- b - 2a)f(x)g(x) + (2b + a)f(x) g(x) + a f(x) )h(x)y(x) +--R + +--R 3 2 2 3 +--R (b f(x)g(x) + (- b + a)f(x) g(x) - a f(x) g(x))h(x) +--R / +--R (b + a)g(x) + (- b - a)f(x) +--R Type: Expression Integer +--E 5 + +--S 6 of 120 +ode51a:=solve(ode51,y,x) +--R +--R (6) "failed" +--R Type: Union("failed",...) +--E 6 + +--S 7 of 120 +ode52 := D(y(x),x) - a*y(x)**n - b*x**(n/(1-n)) +--R +--R n +--R - ----- +--R , n n - 1 +--R (7) y (x) - a y(x) - b x +--R +--R Type: Expression Integer +--E 7 + +--S 8 of 120 +ode52a:=solve(ode52,y,x) +--R +--R (8) "failed" +--R Type: Union("failed",...) +--E 8 + +--S 9 of 120 +ode53 := D(y(x),x) - f(x)**(1-n)*D(g(x),x)*y(x)**n/(a*g(x)+b)**n _ + - D(f(x),x)*y(x)/f(x) - f(x)*D(g(x),x) +--R +--R (9) +--R n , +--R f(x)(a g(x) + b) y (x) +--R +--R + +--R - n + 1 n 2 n , n , +--R (- f(x)f(x) y(x) - f(x) (a g(x) + b) )g (x) - y(x)(a g(x) + b) f (x) +--R +--R / +--R n +--R f(x)(a g(x) + b) +--R Type: Expression Integer +--E 9 + +--S 10 of 120 +ode53a:=solve(ode53,y,x) +--R +--R (10) "failed" +--R Type: Union("failed",...) +--E 10 + +--S 11 of 120 +ode54 := D(y(x),x) - a**n*f(x)**(1-n)*D(g(x),x)*y(x)**n - _ + D(f(x),x)*y(x)/f(x) - f(x)*D(g(x),x) +--R +--R , n - n + 1 n 2 , , +--R f(x)y (x) + (- f(x)a f(x) y(x) - f(x) )g (x) - y(x)f (x) +--R +--R (11) --------------------------------------------------------------- +--R f(x) +--R Type: Expression Integer +--E 11 + +--S 12 of 120 +ode54a:=solve(ode54,y,x) +--R +--R (12) "failed" +--R Type: Union("failed",...) +--E 12 + +--S 13 of 120 +ode55 := D(y(x),x) - f(x)*y(x)**n - g(x)*y(x) - h(x) +--R +--R , n +--R (13) y (x) - f(x)y(x) - g(x)y(x) - h(x) +--R +--R Type: Expression Integer +--E 13 + +--S 14 of 120 +ode55a:=solve(ode55,y,x) +--R +--R (14) "failed" +--R Type: Union("failed",...) +--E 14 + +--S 15 of 120 +ode56 := D(y(x),x) - f(x)*y(x)**a - g(x)*y(x)**b +--R +--R , b a +--R (15) y (x) - g(x)y(x) - f(x)y(x) +--R +--R Type: Expression Integer +--E 15 + +--S 16 of 120 +ode5a:=solve(ode56,y,x) +--R +--R (16) "failed" +--R Type: Union("failed",...) +--E 16 + +--S 17 of 120 +ode57 := D(y(x),x) - sqrt(abs(y(x))) +--R +--R +---------+ , +--R (17) - \|abs(y(x)) + y (x) +--R +--R Type: Expression Integer +--E 17 + +--S 18 of 120 +yx:=solve(ode57,y,x) +--R +--R +---------+ +--R - x\|abs(y(x)) + 2y(x) +--R (18) ----------------------- +--R +----+ +--R \|y(x) +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 120 +ode57expr := D(yx,x) - sqrt(abs(yx)) +--R +--R (19) +--R +--------------------------+ +--R | +---------+ +--R +----+ +---------+ | x\|abs(y(x)) - 2y(x) , +---------+ +--R - \|y(x) \|abs(y(x)) |abs(---------------------) + y (x)\|abs(y(x)) +--R | +----+ +--R \| \|y(x) +--R + +--R - abs(y(x)) +--R / +--R +----+ +---------+ +--R \|y(x) \|abs(y(x)) +--R Type: Expression Integer +--E 19 + +--S 20 of 120 +ode58 := D(y(x),x) - a*sqrt(y(x)) - b*x +--R +--R , +----+ +--R (20) y (x) - a\|y(x) - b x +--R +--R Type: Expression Integer +--E 20 + +--S 21 of 120 +ode58a:=solve(ode58,y,x) +--R +--R (21) "failed" +--R Type: Union("failed",...) +--E 21 + +-- this never finishes +-- ode59 := D(y(x),x) - a*sqrt(y(x)**2+1) - b +-- + +--S 22 of 120 +ode60 := D(y(x),x) - sqrt(y(x)**2-1)/sqrt(x**2-1) +--R +--R +------+ +---------+ +--R | 2 , | 2 +--R \|x - 1 y (x) - \|y(x) - 1 +--R +--R (22) ----------------------------- +--R +------+ +--R | 2 +--R \|x - 1 +--R Type: Expression Integer +--E 22 + +--S 23 of 120 +ode60a:=solve(ode60,y,x) +--R +--R (23) "failed" +--R Type: Union("failed",...) +--E 23 + +--S 24 of 120 +ode61 := D(y(x),x) - sqrt(x**2-1)/sqrt(y(x)**2-1) +--R +--R +---------+ +------+ +--R | 2 , | 2 +--R \|y(x) - 1 y (x) - \|x - 1 +--R +--R (24) ----------------------------- +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R Type: Expression Integer +--E 24 + +--S 25 of 120 +yx:=solve(ode61,y,x) +--R +--R (25) +--R +------+ +---------+ +--R | 2 2 | 2 +--R (4x y(x)\|x - 1 + (- 4x + 2)y(x))\|y(x) - 1 +--R + +--R +------+ +--R 2 | 2 2 2 2 +--R (- 4x y(x) + 2x)\|x - 1 + (4x - 2)y(x) - 2x + 1 +--R * +--R +---------+ +--R | 2 +--R log(\|y(x) - 1 - y(x)) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (- 4x y(x)\|x - 1 + (4x - 2)y(x))log(\|x - 1 - x) +--R + +--R +------+ +--R 3 3 | 2 2 3 +--R (- 4x y(x) + 4x y(x))\|x - 1 + (4x - 2)y(x) +--R + +--R 4 2 +--R (- 4x + 2x + 1)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R +------+ +------+ +--R 2 | 2 2 2 2 | 2 +--R ((4x y(x) - 2x)\|x - 1 + (- 4x + 2)y(x) + 2x - 1)log(\|x - 1 - x) +--R + +--R +------+ +--R 4 3 2 3 | 2 2 4 +--R (4x y(x) + (- 4x - 2x)y(x) + 2x - x)\|x - 1 + (- 4x + 2)y(x) +--R + +--R 4 2 4 2 +--R (4x - 2)y(x) - 2x + 2x +--R / +--R +------+ +---------+ +--R | 2 2 | 2 +--R (8x y(x)\|x - 1 + (- 8x + 4)y(x))\|y(x) - 1 +--R + +--R +------+ +--R 2 | 2 2 2 2 +--R (- 8x y(x) + 4x)\|x - 1 + (8x - 4)y(x) - 4x + 2 +--R Type: Union(Expression Integer,...) +--E 25 + +--S 26 of 120 +ode61expr := D(yx,x) - sqrt(x**2-1)/sqrt(yx**2-1) +--R +--R (26) +--R 4 2 5 4 2 3 +--R (- 64x + 64x - 8)y(x) + (96x - 96x + 12)y(x) +--R + +--R 4 2 +--R (- 32x + 32x - 4)y(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 5 3 5 5 3 3 +--R (64x - 96x + 32x)y(x) + (- 96x + 144x - 48x)y(x) +--R + +--R 5 3 +--R (32x - 48x + 16x)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 4 2 6 4 2 4 +--R (64x - 64x + 8)y(x) + (- 128x + 128x - 16)y(x) +--R + +--R 4 2 2 4 2 +--R (72x - 72x + 9)y(x) - 8x + 8x - 1 +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 5 3 6 5 3 4 +--R (- 64x + 96x - 32x)y(x) + (128x - 192x + 64x)y(x) +--R + +--R 5 3 2 5 3 +--R (- 72x + 108x - 36x)y(x) + 8x - 12x + 4x +--R * +--R , +--R y (x) +--R +--R + +--R 5 3 4 5 3 2 5 +--R (64x - 96x + 32x)y(x) + (- 64x + 96x - 32x)y(x) + 8x +--R + +--R 3 +--R - 12x + 4x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 6 4 2 4 6 4 2 2 +--R (- 64x + 128x - 72x + 8)y(x) + (64x - 128x + 72x - 8)y(x) +--R + +--R 6 4 2 +--R - 8x + 16x - 9x + 1 +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 5 3 5 5 3 3 +--R (- 64x + 96x - 32x)y(x) + (96x - 144x + 48x)y(x) +--R + +--R 5 3 +--R (- 32x + 48x - 16x)y(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 6 4 2 5 6 4 2 3 +--R (64x - 128x + 72x - 8)y(x) + (- 96x + 192x - 108x + 12)y(x) +--R + +--R 6 4 2 +--R (32x - 64x + 36x - 4)y(x) +--R * +--R ROOT +--R +------+ +--R 3 3 3 | 2 +--R ((64x - 32x)y(x) + (- 32x + 16x)y(x))\|x - 1 +--R + +--R 4 2 3 4 2 +--R (- 64x + 64x - 8)y(x) + (32x - 32x + 4)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 3 4 3 2 3 +--R ((- 64x + 32x)y(x) + (64x - 32x)y(x) - 8x + 4x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 4 4 2 2 4 +--R (64x - 64x + 8)y(x) + (- 64x + 64x - 8)y(x) + 8x +--R + +--R 2 +--R - 8x + 1 +--R * +--R +---------+ 2 +--R | 2 +--R log(\|y(x) - 1 - y(x)) +--R + +--R +------+ +--R 3 3 3 | 2 +--R ((- 128x + 64x)y(x) + (64x - 32x)y(x))\|x - 1 +--R + +--R 4 2 3 4 2 +--R (128x - 128x + 16)y(x) + (- 64x + 64x - 8)y(x) +--R * +--R +------+ +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 5 5 3 +--R (- 128x + 64x)y(x) + (128x - 48x)y(x) +--R + +--R 5 3 +--R (- 64x + 48x )y(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 5 +--R (128x - 128x + 16)y(x) +--R + +--R 6 4 2 3 +--R (- 128x + 64x + 64x - 16)y(x) +--R + +--R 6 4 2 +--R (64x - 80x + 16x + 2)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 3 4 3 2 3 +--R (128x - 64x)y(x) + (- 128x + 64x)y(x) + 16x +--R + +--R - 8x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 4 4 2 2 +--R (- 128x + 128x - 16)y(x) + (128x - 128x + 16)y(x) +--R + +--R 4 2 +--R - 16x + 16x - 2 +--R * +--R +------+ +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 6 5 3 4 +--R (128x - 64x)y(x) + (- 128x - 64x + 80x)y(x) +--R + +--R 5 3 2 5 3 +--R (128x - 64x - 16x)y(x) - 16x + 16x - 2x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 6 6 2 4 +--R (- 128x + 128x - 16)y(x) + (128x - 128x + 24)y(x) +--R + +--R 6 4 2 6 4 2 +--R (- 128x + 128x - 8)y(x) + 16x - 24x + 8x +--R * +--R +---------+ +--R | 2 +--R log(\|y(x) - 1 - y(x)) +--R + +--R +------+ +--R 3 3 3 | 2 +--R ((64x - 32x)y(x) + (- 32x + 16x)y(x))\|x - 1 +--R + +--R 4 2 3 4 2 +--R (- 64x + 64x - 8)y(x) + (32x - 32x + 4)y(x) +--R * +--R +------+ 2 +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 5 5 3 +--R (128x - 64x)y(x) + (- 128x + 48x)y(x) +--R + +--R 5 3 +--R (64x - 48x )y(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 5 +--R (- 128x + 128x - 16)y(x) +--R + +--R 6 4 2 3 +--R (128x - 64x - 64x + 16)y(x) +--R + +--R 6 4 2 +--R (- 64x + 80x - 16x - 2)y(x) +--R * +--R +------+ +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 7 5 3 5 +--R (64x - 32x)y(x) + (- 128x + 32x + 32x)y(x) +--R + +--R 7 5 3 3 +--R (64x + 32x - 320x + 128x)y(x) +--R + +--R 7 5 3 +--R (- 32x + 32x + 128x - 66x)y(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 7 6 4 2 5 +--R (- 64x + 64x - 8)y(x) + (128x - 96x - 32x + 12)y(x) +--R + +--R 8 4 2 3 +--R (- 64x + 344x - 280x + 28)y(x) +--R + +--R 8 6 4 2 +--R (32x - 48x - 116x + 132x - 16)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 3 4 3 2 3 +--R ((- 64x + 32x)y(x) + (64x - 32x)y(x) - 8x + 4x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 4 4 2 2 4 +--R (64x - 64x + 8)y(x) + (- 64x + 64x - 8)y(x) + 8x +--R + +--R 2 +--R - 8x + 1 +--R * +--R +------+ 2 +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 6 5 3 4 +--R (- 128x + 64x)y(x) + (128x + 64x - 80x)y(x) +--R + +--R 5 3 2 5 3 +--R (- 128x + 64x + 16x)y(x) + 16x - 16x + 2x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 6 6 2 4 +--R (128x - 128x + 16)y(x) + (- 128x + 128x - 24)y(x) +--R + +--R 6 4 2 6 4 2 +--R (128x - 128x + 8)y(x) - 16x + 24x - 8x +--R * +--R +------+ +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 8 5 6 +--R (- 64x + 32x)y(x) + (128x - 48x)y(x) +--R + +--R 7 5 3 4 +--R (- 64x - 96x + 344x - 116x)y(x) +--R + +--R 7 5 3 2 7 5 3 +--R (64x - 32x - 280x + 132x)y(x) - 8x + 12x + 28x - 16x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 8 6 4 2 6 +--R (64x - 64x + 8)y(x) + (- 128x + 64x + 64x - 16)y(x) +--R + +--R 8 6 4 2 4 +--R (64x + 64x - 400x + 272x - 23)y(x) +--R + +--R 8 6 4 2 2 8 6 4 +--R (- 64x + 64x + 272x - 272x + 31)y(x) + 8x - 16x - 23x +--R + +--R 2 +--R 31x - 4 +--R / +--R +------+ +--R 3 3 3 | 2 +--R ((256x - 128x)y(x) + (- 128x + 64x)y(x))\|x - 1 +--R + +--R 4 2 3 4 2 +--R (- 256x + 256x - 32)y(x) + (128x - 128x + 16)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 3 4 3 2 3 +--R ((- 256x + 128x)y(x) + (256x - 128x)y(x) - 32x + 16x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 4 4 2 2 4 +--R (256x - 256x + 32)y(x) + (- 256x + 256x - 32)y(x) + 32x +--R + +--R 2 +--R - 32x + 4 +--R + +--R 5 3 4 5 3 2 5 +--R (64x - 96x + 32x)y(x) + (- 64x + 96x - 32x)y(x) + 8x +--R + +--R 3 +--R - 12x + 4x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 6 4 2 4 6 4 2 2 +--R (- 64x + 128x - 72x + 8)y(x) + (64x - 128x + 72x - 8)y(x) +--R + +--R 6 4 2 +--R - 8x + 16x - 9x + 1 +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 5 3 5 5 3 3 +--R (- 64x + 96x - 32x)y(x) + (96x - 144x + 48x)y(x) +--R + +--R 5 3 +--R (- 32x + 48x - 16x)y(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 6 4 2 5 6 4 2 3 +--R (64x - 128x + 72x - 8)y(x) + (- 96x + 192x - 108x + 12)y(x) +--R + +--R 6 4 2 +--R (32x - 64x + 36x - 4)y(x) +--R / +--R 4 2 4 4 2 2 4 2 +--R (64x - 64x + 8)y(x) + (- 64x + 64x - 8)y(x) + 8x - 8x +--R + +--R 1 +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 5 3 4 5 3 2 5 3 +--R (- 64x + 96x - 32x)y(x) + (64x - 96x + 32x)y(x) - 8x + 12x +--R + +--R - 4x +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 4 2 5 4 2 3 +--R (- 64x + 64x - 8)y(x) + (96x - 96x + 12)y(x) +--R + +--R 4 2 +--R (- 32x + 32x - 4)y(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 5 3 5 5 3 3 +--R (64x - 96x + 32x)y(x) + (- 96x + 144x - 48x)y(x) +--R + +--R 5 3 +--R (32x - 48x + 16x)y(x) +--R * +--R ROOT +--R +------+ +--R 3 3 3 | 2 +--R ((64x - 32x)y(x) + (- 32x + 16x)y(x))\|x - 1 +--R + +--R 4 2 3 4 2 +--R (- 64x + 64x - 8)y(x) + (32x - 32x + 4)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R +------+ +--R 3 4 3 2 3 | 2 +--R ((- 64x + 32x)y(x) + (64x - 32x)y(x) - 8x + 4x)\|x - 1 +--R + +--R 4 2 4 4 2 2 4 2 +--R (64x - 64x + 8)y(x) + (- 64x + 64x - 8)y(x) + 8x - 8x +--R + +--R 1 +--R * +--R +---------+ 2 +--R | 2 +--R log(\|y(x) - 1 - y(x)) +--R + +--R +------+ +--R 3 3 3 | 2 +--R ((- 128x + 64x)y(x) + (64x - 32x)y(x))\|x - 1 +--R + +--R 4 2 3 4 2 +--R (128x - 128x + 16)y(x) + (- 64x + 64x - 8)y(x) +--R * +--R +------+ +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 5 5 3 +--R (- 128x + 64x)y(x) + (128x - 48x)y(x) +--R + +--R 5 3 +--R (- 64x + 48x )y(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 5 +--R (128x - 128x + 16)y(x) +--R + +--R 6 4 2 3 +--R (- 128x + 64x + 64x - 16)y(x) +--R + +--R 6 4 2 +--R (64x - 80x + 16x + 2)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 3 4 3 2 3 +--R ((128x - 64x)y(x) + (- 128x + 64x)y(x) + 16x - 8x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 4 4 2 2 +--R (- 128x + 128x - 16)y(x) + (128x - 128x + 16)y(x) +--R + +--R 4 2 +--R - 16x + 16x - 2 +--R * +--R +------+ +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 6 5 3 4 +--R (128x - 64x)y(x) + (- 128x - 64x + 80x)y(x) +--R + +--R 5 3 2 5 3 +--R (128x - 64x - 16x)y(x) - 16x + 16x - 2x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 6 6 2 4 +--R (- 128x + 128x - 16)y(x) + (128x - 128x + 24)y(x) +--R + +--R 6 4 2 6 4 2 +--R (- 128x + 128x - 8)y(x) + 16x - 24x + 8x +--R * +--R +---------+ +--R | 2 +--R log(\|y(x) - 1 - y(x)) +--R + +--R +------+ +--R 3 3 3 | 2 +--R ((64x - 32x)y(x) + (- 32x + 16x)y(x))\|x - 1 +--R + +--R 4 2 3 4 2 +--R (- 64x + 64x - 8)y(x) + (32x - 32x + 4)y(x) +--R * +--R +------+ 2 +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 5 5 3 +--R (128x - 64x)y(x) + (- 128x + 48x)y(x) +--R + +--R 5 3 +--R (64x - 48x )y(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 5 +--R (- 128x + 128x - 16)y(x) +--R + +--R 6 4 2 3 +--R (128x - 64x - 64x + 16)y(x) +--R + +--R 6 4 2 +--R (- 64x + 80x - 16x - 2)y(x) +--R * +--R +------+ +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 7 5 3 5 +--R (64x - 32x)y(x) + (- 128x + 32x + 32x)y(x) +--R + +--R 7 5 3 3 +--R (64x + 32x - 320x + 128x)y(x) +--R + +--R 7 5 3 +--R (- 32x + 32x + 128x - 66x)y(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 7 6 4 2 5 +--R (- 64x + 64x - 8)y(x) + (128x - 96x - 32x + 12)y(x) +--R + +--R 8 4 2 3 +--R (- 64x + 344x - 280x + 28)y(x) +--R + +--R 8 6 4 2 +--R (32x - 48x - 116x + 132x - 16)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R +------+ +--R 3 4 3 2 3 | 2 +--R ((- 64x + 32x)y(x) + (64x - 32x)y(x) - 8x + 4x)\|x - 1 +--R + +--R 4 2 4 4 2 2 4 2 +--R (64x - 64x + 8)y(x) + (- 64x + 64x - 8)y(x) + 8x - 8x +--R + +--R 1 +--R * +--R +------+ 2 +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 6 5 3 4 +--R (- 128x + 64x)y(x) + (128x + 64x - 80x)y(x) +--R + +--R 5 3 2 5 3 +--R (- 128x + 64x + 16x)y(x) + 16x - 16x + 2x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 6 6 2 4 +--R (128x - 128x + 16)y(x) + (- 128x + 128x - 24)y(x) +--R + +--R 6 4 2 6 4 2 +--R (128x - 128x + 8)y(x) - 16x + 24x - 8x +--R * +--R +------+ +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 8 5 6 +--R (- 64x + 32x)y(x) + (128x - 48x)y(x) +--R + +--R 7 5 3 4 +--R (- 64x - 96x + 344x - 116x)y(x) +--R + +--R 7 5 3 2 7 5 3 +--R (64x - 32x - 280x + 132x)y(x) - 8x + 12x + 28x - 16x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 8 6 4 2 6 +--R (64x - 64x + 8)y(x) + (- 128x + 64x + 64x - 16)y(x) +--R + +--R 8 6 4 2 4 +--R (64x + 64x - 400x + 272x - 23)y(x) +--R + +--R 8 6 4 2 2 8 6 4 +--R (- 64x + 64x + 272x - 272x + 31)y(x) + 8x - 16x - 23x +--R + +--R 2 +--R 31x - 4 +--R / +--R +------+ +--R 3 3 3 | 2 +--R ((256x - 128x)y(x) + (- 128x + 64x)y(x))\|x - 1 +--R + +--R 4 2 3 4 2 +--R (- 256x + 256x - 32)y(x) + (128x - 128x + 16)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 3 4 3 2 3 +--R ((- 256x + 128x)y(x) + (256x - 128x)y(x) - 32x + 16x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 4 4 2 2 4 +--R (256x - 256x + 32)y(x) + (- 256x + 256x - 32)y(x) + 32x +--R + +--R 2 +--R - 32x + 4 +--R Type: Expression Integer +--E 26 + +--S 27 of 120 +ode62 := D(y(x),x) - (y(x)-x**2*sqrt(x**2-y(x)**2))/_ + (x*y(x)*sqrt(x**2-y(x)**2)+x) +--R +--R +------------+ +------------+ +--R | 2 2 , 2 | 2 2 +--R (x y(x)\|- y(x) + x + x)y (x) + x \|- y(x) + x - y(x) +--R +--R (27) ----------------------------------------------------------- +--R +------------+ +--R | 2 2 +--R x y(x)\|- y(x) + x + x +--R Type: Expression Integer +--E 27 + +--S 28 of 120 +ode62a:=solve(ode62,y,x) +--R +--R (28) "failed" +--R Type: Union("failed",...) +--E 28 + +--S 29 of 120 +ode63 := D(y(x),x) - (1+ y(x)**2)/(abs(y(x)+sqrt(1+y(x)))*sqrt(1+x)**3) +--R +--R +-----+ , +--------+ 2 +--R (x + 1)\|x + 1 y (x)abs(\|y(x) + 1 + y(x)) - y(x) - 1 +--R +--R (29) ------------------------------------------------------- +--R +-----+ +--------+ +--R (x + 1)\|x + 1 abs(\|y(x) + 1 + y(x)) +--R Type: Expression Integer +--E 29 + +--S 30 of 120 +ode63a:=solve(ode63,y,x) +--R +--R (30) "failed" +--R Type: Union("failed",...) +--E 30 + +--S 31 of 120 +ode64 := D(y(x),x) - sqrt((a*y(x)**2+b*y(x)+c)/(a*x**2+b*x+c)) +--R +--R +--------------------+ +--R | 2 +--R , |a y(x) + b y(x) + c +--R (31) y (x) - |-------------------- +--R | 2 +--R \| a x + b x + c +--R Type: Expression Integer +--E 31 + +--S 32 of 120 +yx:=solve(ode64,y,x) +--R +--R (32) +--R log +--R +--------------------+ +--R | 2 +--R 2 2 +-+ |a y(x) + b y(x) + c +--R (2a x + 2a b x + 2a c)\|a |-------------------- +--R | 2 +--R \| a x + b x + c +--R * +--R +--------------------+ +--R | 2 +--R \|a y(x) + b y(x) + c +--R + +--R 3 3 2 2 2 2 +--R (- 2a x - 2a b x - 2a c x)y(x) +--R + +--R 2 3 2 2 2 3 2 +--R (- 2a b x - 2a b x - 2a b c x)y(x) - 2a c x - 2a b c x +--R + +--R 2 +--R - 2a c x +--R * +--R +-------------------------+ +--R | 2 2 +--R \|a c y(x) + b c y(x) + c +--R + +--R 3 4 2 3 2 2 2 3 2 +--R (- a x - a b x - 2a c x - a b c x - a c - a )y(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (- a b x - a b x - 2a b c x - b c x - b c - a b)y(x) +--R + +--R 2 4 3 2 2 2 3 2 +--R - a c x - a b c x - 2a c x - b c x - c - a c +--R * +--R +--------------------+ +--R +-+ | 2 +--R \|a \|a y(x) + b y(x) + c +--R + +--R 4 3 3 2 3 2 +--R (2a x + 2a b x + 2a c x)y(x) +--R + +--R 3 3 2 2 2 2 3 3 2 2 +--R (2a b x + 2a b x + 2a b c x)y(x) + 2a c x + 2a b c x +--R + +--R 2 2 +--R 2a c x +--R * +--R +--------------------+ +--R | 2 +--R |a y(x) + b y(x) + c +--R |-------------------- +--R | 2 +--R \| a x + b x + c +--R / +--R +--------------------+ +--R | 2 +--R 2 2 |a y(x) + b y(x) + c +--R (2a x + 2a b x + 2a c) |-------------------- +--R | 2 +--R \| a x + b x + c +--R * +--R +-------------------------+ +--R | 2 2 +--R \|a c y(x) + b c y(x) + c +--R + +--R 3 4 2 3 2 3 2 +--R (a x + a b x - a b c x - a c - a )y(x) +--R + +--R 2 4 2 3 2 2 2 2 4 3 +--R (a b x + a b x - b c x - b c - a b)y(x) + a c x + a b c x +--R + +--R 2 3 2 +--R - b c x - c - a c +--R + +--R log +--R +--------------------+ +--R +-+ +-+ | 2 +-+ +--R (2\|a \|c - 2a y(x))\|a y(x) + b y(x) + c + 2a y(x)\|c +--R + +--R 2 +-+ +--R (- 2a y(x) - b y(x) - 2c)\|a +--R / +--R +--------------------+ +--R +-+ | 2 +--R 2\|c \|a y(x) + b y(x) + c - b y(x) - 2c +--R / +--R +-+ +--R \|a +--R Type: Union(Expression Integer,...) +--E 32 + +@ +The results of this substitution are too long to include. +It should be zero but Axiom cannot simplify it. +<<*>>= +--S 33 of 120 +ode64expr := D(yx,x) - sqrt((a*yx**2+b*yx+c)/(a*x**2+b*x+c)); +--E 33 + +--S 34 of 120 +ode65 := D(y(x),x) - sqrt((y(x)**3+1)/(x**3+1)) +--R +--R +---------+ +--R | 3 +--R , |y(x) + 1 +--R (34) y (x) - |--------- +--R | 3 +--R \| x + 1 +--R Type: Expression Integer +--E 34 + +--S 35 of 120 +ode65a:=solve(ode65,y,x) +--R +--R +---------+ +--R | 3 +--R |y(x) + 1 +--R |--------- +--R x | 3 y(x) +--I ++ \| %P + 1 ++ 1 +--I (35) | - ------------ d%P + | ---------- d%P +--R ++ +---------+ ++ +-------+ +--R | 3 | 3 +--I \|y(x) + 1 \|%P + 1 +--R Type: Union(Expression Integer,...) +--E 35 + +--S 36 of 120 +ode66 := D(y(x),x) - sqrt(abs(y(x)*(1-y(x))*(1-a*y(x))))/_ + sqrt(abs(x*(1-x)*(1-a*x))) +--R +--R (36) +--R +------------------------------------+ +--R | 3 2 +--R - \|abs(a y(x) + (- a - 1)y(x) + y(x)) +--R + +--R +---------------------------+ +--R | 3 2 , +--R \|abs(a x + (- a - 1)x + x) y (x) +--R +--R / +--R +---------------------------+ +--R | 3 2 +--R \|abs(a x + (- a - 1)x + x) +--R Type: Expression Integer +--E 36 + +--S 37 of 120 +ode66a:=solve(ode66,y,x) +--R +--R (37) "failed" +--R Type: Union("failed",...) +--E 37 + +--S 38 of 120 +ode67 := D(y(x),x) - sqrt(1-y(x)**4)/sqrt(1-x**4) +--R +--R +--------+ +-----------+ +--R | 4 , | 4 +--R \|- x + 1 y (x) - \|- y(x) + 1 +--R +--R (38) --------------------------------- +--R +--------+ +--R | 4 +--R \|- x + 1 +--R Type: Expression Integer +--E 38 + +--S 39 of 120 +ode67a:=solve(ode67,y,x) +--R +--R (39) "failed" +--R Type: Union("failed",...) +--E 39 + +--S 40 of 120 +ode68 := D(y(x),x) - sqrt((a*y(x)**4+b*y(x)**2+1)/(a*x**4+b*x**2+1)) +--R +--R +---------------------+ +--R | 4 2 +--R , |a y(x) + b y(x) + 1 +--R (40) y (x) - |--------------------- +--R | 4 2 +--R \| a x + b x + 1 +--R Type: Expression Integer +--E 40 + +--S 41 of 120 +ode68a:=solve(ode68,y,x) +--R +--R +--R (41) +--R +---------------------+ +--R | 4 2 +--R |a y(x) + b y(x) + 1 +--R |--------------------- +--R x | 2 4 y(x) +--I ++ \| %N b + %N a + 1 ++ 1 +--I | - ------------------------ d%N + | ------------------ d%N +--R ++ +---------------------+ ++ +---------------+ +--R | 4 2 | 2 4 +--I \|a y(x) + b y(x) + 1 \|%N b + %N a + 1 +--R Type: Union(Expression Integer,...) +--E 41 + +--S 42 of 120 +ode69 := D(y(x),x) - sqrt((b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)*_ + (a4*x**4+a3*x**3+a2*x**2+a1*x+a0)) +--R +--R +--R (42) +--R , +--R y (x) +--R +--R + +--R - +--R ROOT +--R 4 3 2 4 +--R (a4 b4 x + a3 b4 x + a2 b4 x + a1 b4 x + a0 b4)y(x) +--R + +--R 4 3 2 3 +--R (a4 b3 x + a3 b3 x + a2 b3 x + a1 b3 x + a0 b3)y(x) +--R + +--R 4 3 2 2 +--R (a4 b2 x + a3 b2 x + a2 b2 x + a1 b2 x + a0 b2)y(x) +--R + +--R 4 3 2 4 +--R (a4 b1 x + a3 b1 x + a2 b1 x + a1 b1 x + a0 b1)y(x) + a4 b0 x +--R + +--R 3 2 +--R a3 b0 x + a2 b0 x + a1 b0 x + a0 b0 +--R Type: Expression Integer +--E 42 + +--S 43 of 120 +ode69a:=solve(ode69,y,x) +--R +--R +--R >> Error detected within library code: +--R PFO::possibleOrder: more than 1 algebraic constant +--R +--R Continuing to read the file... +--R +--E 43 + +--S 44 of 120 +ode70 := D(y(x),x) - sqrt((a4*x**4+a3*x**3+a2*x**2+a1*x+a0)/_ + (b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)) +--R +--R +---------------------------------------------+ +--R | 4 3 2 +--R , | a4 x + a3 x + a2 x + a1 x + a0 +--R (43) y (x) - |--------------------------------------------- +--R | 4 3 2 +--R \|b4 y(x) + b3 y(x) + b2 y(x) + b1 y(x) + b0 +--R Type: Expression Integer +--E 44 + +--S 45 of 120 +ode70a:=solve(ode70,y,x) +--R +--R +--R >> Error detected within library code: +--R PFO::possibleOrder: more than 1 algebraic constant +--R +--R Continuing to read the file... +--R +--E 45 + +--S 46 of 120 +ode71 := D(y(x),x) - sqrt((b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)/_ + (a4*x**4+a3*x**3+a2*x**2+a1*x+a0)) +--R +--R +---------------------------------------------+ +--R | 4 3 2 +--R , |b4 y(x) + b3 y(x) + b2 y(x) + b1 y(x) + b0 +--R (44) y (x) - |--------------------------------------------- +--R | 4 3 2 +--R \| a4 x + a3 x + a2 x + a1 x + a0 +--R Type: Expression Integer +--E 46 + +--S 47 of 120 +ode71a:=solve(ode71,y,x) +--R +--R +--R (45) +--R +---------------------------------------------+ +--R | 4 3 2 +--R |b4 y(x) + b3 y(x) + b2 y(x) + b1 y(x) + b0 +--R |--------------------------------------------- +--R x | 4 3 2 +--I ++ \| %N a4 + %N a3 + %N a2 + %N a1 + a0 +--I | - ------------------------------------------------ d%N +--R ++ +---------------------------------------------+ +--R | 4 3 2 +--R \|b4 y(x) + b3 y(x) + b2 y(x) + b1 y(x) + b0 +--R + +--R y(x) +--R ++ 1 +--I | ------------------------------------- d%N +--R ++ +----------------------------------+ +--R | 4 3 2 +--I \|%N b4 + %N b3 + %N b2 + %N b1 + b0 +--R Type: Union(Expression Integer,...) +--E 47 + +--S 48 of 120 +R1:=operator 'R1 +--R +--R (46) R1 +--R Type: BasicOperator +--E 48 + +--S 49 of 120 +R2:=operator 'R2 +--R +--R (47) R2 +--R Type: BasicOperator +--E 49 + +--S 50 of 120 +ode72 := D(y(x),x) - R1(x,sqrt(a4*x**4+a3*x**3+a2*x**2+a1*x+a0))*_ + R2(y(x),sqrt(b4*y(x)**4+b3*y(x)**3+b2*y(x)**2+b1*y(x)+b0)) +--R +--R (48) +--R - +--R +---------------------------------+ +--R | 4 3 2 +--R R1(x,\|a4 x + a3 x + a2 x + a1 x + a0 ) +--R * +--R +---------------------------------------------+ +--R | 4 3 2 +--R R2(y(x),\|b4 y(x) + b3 y(x) + b2 y(x) + b1 y(x) + b0 ) +--R + +--R , +--R y (x) +--R +--R Type: Expression Integer +--E 50 + +--S 51 of 120 +ode72a:=solve(ode72,y,x) +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 51 + +--S 52 of 120 +ode73 := D(y(x),x) - ((a3*x**3+a2*x**2+a1*x+a0)/_ + (a3*y(x)**3+a2*y(x)**2+a1*y(x)+a0))**(2/3) +--R +--R +----------------------------------+2 +--R | 3 2 +--R , | a3 x + a2 x + a1 x + a0 +--R (49) y (x) - |---------------------------------- +--R 3| 3 2 +--R \|a3 y(x) + a2 y(x) + a1 y(x) + a0 +--R Type: Expression Integer +--E 52 + +@ +Attempting to solve this problem fails with the error: +\begin{verbatim} +ode73a:=solve(ode73,y,x) + >> Error detected within library code: + Table construction failed in MLIFT +\end{verbatim} +<<*>>= + +--S 53 of 120 +ode74 := D(y(x),x) - f(x)*(y(x)-g(x))*sqrt((y(x)-a)*(y(x)-b)) +--R +--R +---------------------------+ +--R , | 2 +--R (50) y (x) + (- f(x)y(x) + f(x)g(x))\|y(x) + (- b - a)y(x) + a b +--R +--R Type: Expression Integer +--E 53 + +--S 54 of 120 +ode74a:=solve(ode74,y,x) +--R +--R (51) "failed" +--R Type: Union("failed",...) +--E 54 + +--S 55 of 120 +ode75 := D(y(x),x) - exp(x-y(x)) + exp(x) +--R +--R , - y(x) + x x +--R (52) y (x) - %e + %e +--R +--R Type: Expression Integer +--E 55 + +--S 56 of 120 +ode75a:=solve(ode75,y,x) +--R +--R (53) "failed" +--R Type: Union("failed",...) +--E 56 + +--S 57 of 120 +ode76 := D(y(x),x) - a*cos(y(x)) + b +--R +--R , +--R (54) y (x) - a cos(y(x)) + b +--R +--R Type: Expression Integer +--E 57 + +--S 58 of 120 +yx:=solve(ode76,y,x) +--R +--R (55) +--R +---------+ +---------+ +--R 2 2 | 2 2 | 2 2 +--R (- b + a )sin(y(x)) + b\|- b + a cos(y(x)) - a\|- b + a +--R log(-------------------------------------------------------------) +--R a cos(y(x)) - b +--R + +--R +---------+ +--R | 2 2 +--R x\|- b + a +--R / +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 of 120 +ode76expr := D(yx,x) - a*cos(yx) + b +--R +--R (56) +--R 2 2 4 3 3 +--R ((- a b + a )cos(y(x)) + a b - a b)sin(y(x)) +--R + +--R +---------+ +---------+ +--R 2 | 2 2 2 2 3 | 2 2 +--R a b\|- b + a cos(y(x)) + (- a b - a )\|- b + a cos(y(x)) +--R + +--R +---------+ +--R 2 | 2 2 +--R a b\|- b + a +--R * +--R cos +--R log +--R +---------+ +---------+ +--R 2 2 | 2 2 | 2 2 +--R (- b + a )sin(y(x)) + b\|- b + a cos(y(x)) - a\|- b + a +--R ------------------------------------------------------------- +--R a cos(y(x)) - b +--R + +--R +---------+ +--R | 2 2 +--R x\|- b + a +--R / +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 2 2 2 +--R - a\|- b + a sin(y(x)) + (- b + a )sin(y(x)) +--R + +--R +---------+ +---------+ +--R | 2 2 2 | 2 2 +--R - a\|- b + a cos(y(x)) + b\|- b + a cos(y(x)) +--R * +--R , +--R y (x) +--R +--R + +--R 3 2 3 3 4 3 2 2 2 +--R ((a b + a b - a b - a )cos(y(x)) - b - b + a b + a b)sin(y(x)) +--R + +--R +---------+ +--R 2 | 2 2 2 +--R (- a b - a b)\|- b + a cos(y(x)) +--R + +--R +---------+ +---------+ +--R 3 2 2 2 | 2 2 2 | 2 2 +--R (b + b + a b + a )\|- b + a cos(y(x)) + (- a b - a b)\|- b + a +--R / +--R +---------+ +--R 2 3 3 2 | 2 2 2 +--R ((a b - a )cos(y(x)) - b + a b)sin(y(x)) - a b\|- b + a cos(y(x)) +--R + +--R +---------+ +---------+ +--R 2 2 | 2 2 | 2 2 +--R (b + a )\|- b + a cos(y(x)) - a b\|- b + a +--R Type: Expression Integer +--E 59 + +--S 60 of 120 +ode77 := D(y(x),x) - cos(a*y(x)+b*x) +--R +--R , +--R (57) y (x) - cos(a y(x) + b x) +--R +--R Type: Expression Integer +--E 60 + +--S 61 of 120 +ode77a:=solve(ode77,y,x) +--R +--R (58) "failed" +--R Type: Union("failed",...) +--E 61 + +--S 62 of 120 +ode78 := D(y(x),x) + a*sin(alpha*y(x)+beta*x) + b +--R +--R , +--R (59) y (x) + a sin(alpha y(x) + beta x) + b +--R +--R Type: Expression Integer +--E 62 + +--S 63 of 120 +ode78a:=solve(ode78,y,x) +--R +--R (60) "failed" +--R Type: Union("failed",...) +--E 63 + +--S 64 of 120 +ode79 := D(y(x),x) + f(x)*cos(a*y(x)) + g(x)*sin(a*y(x)) + h(x) +--R +--R , +--R (61) y (x) + g(x)sin(a y(x)) + f(x)cos(a y(x)) + h(x) +--R +--R Type: Expression Integer +--E 64 + +--S 65 of 120 +ode79a:=solve(ode79,y,x) +--R +--R (62) "failed" +--R Type: Union("failed",...) +--E 65 + +--S 66 of 120 +ode80 := D(y(x),x) + f(x)*sin(y(x)) + (1-D(f(x),x))*cos(y(x)) - D(f(x),x) - 1 +--R +--R , , +--R (63) y (x) + (- cos(y(x)) - 1)f (x) + f(x)sin(y(x)) + cos(y(x)) - 1 +--R +--R Type: Expression Integer +--E 66 + +--S 67 of 120 +ode80a:=solve(ode80,y,x) +--R +--R (64) "failed" +--R Type: Union("failed",...) +--E 67 + +--S 68 of 120 +ode81 := D(y(x),x) + 2*tan(y(x))*tan(x) - 1 +--R +--R , +--R (65) y (x) + 2tan(x)tan(y(x)) - 1 +--R +--R Type: Expression Integer +--E 68 + +--S 69 of 120 +ode81a:=solve(ode81,y,x) +--R +--R (66) "failed" +--R Type: Union("failed",...) +--E 69 + +--S 70 of 120 +ode82 := D(y(x),x) - a*(1+tan(y(x))**2) + tan(y(x))*tan(x) +--R +--R , 2 +--R (67) y (x) - a tan(y(x)) + tan(x)tan(y(x)) - a +--R +--R Type: Expression Integer +--E 70 + +--S 71 of 120 +ode82a:=solve(ode82,y,x) +--R +--R (68) "failed" +--R Type: Union("failed",...) +--E 71 + +--S 72 of 120 +ode83 := D(y(x),x) - tan(x*y(x)) +--R +--R , +--R (69) y (x) - tan(x y(x)) +--R +--R Type: Expression Integer +--E 72 + +--S 73 of 120 +ode83a:=solve(ode83,y,x) +--R +--R (70) "failed" +--R Type: Union("failed",...) +--E 73 + +--S 74 of 120 +ode84 := D(y(x),x) - f(a*x + b*y(x)) +--R +--R , +--R (71) y (x) - f(b y(x) + a x) +--R +--R Type: Expression Integer +--E 74 + +--S 75 of 120 +ode84a:=solve(ode84,y,x) +--R +--R (72) "failed" +--R Type: Union("failed",...) +--E 75 + +--S 76 of 120 +ode85 := D(y(x),x) - x**(a-1)*y(x)**(1-b)*f(x**a/a + y(x)**b/b) +--R +--R b a +--R a - 1 - b + 1 a y(x) + b x , +--R (73) - x y(x) f(--------------) + y (x) +--R a b +--R Type: Expression Integer +--E 76 + +--S 77 of 120 +ode85a:=solve(ode85,y,x) +--R +--R (74) "failed" +--R Type: Union("failed",...) +--E 77 + +--S 78 of 120 +ode86 := D(y(x),x) - (y(x)-x*f(x**2+a*y(x)**2))/(x+a*y(x)*f(x**2+a*y(x)**2)) +--R +--R 2 2 , 2 2 +--R (a y(x)f(a y(x) + x ) + x)y (x) + x f(a y(x) + x ) - y(x) +--R +--R (75) ----------------------------------------------------------- +--R 2 2 +--R a y(x)f(a y(x) + x ) + x +--R Type: Expression Integer +--E 78 + +--S 79 of 120 +ode86a:=solve(ode86,y,x) +--R +--R (76) "failed" +--R Type: Union("failed",...) +--E 79 + +--S 80 of 120 +ode87 := D(y(x),x) - (y(x)*a*f(x**c*y(x))+c*x**a*y(x)**b)/_ + (x*b*f(x**c*y(x))-x**a*y(x)**b) +--R +--R a b c , a b c +--R (x y(x) - b x f(y(x)x ))y (x) + c x y(x) + a y(x)f(y(x)x ) +--R +--R (77) ------------------------------------------------------------ +--R a b c +--R x y(x) - b x f(y(x)x ) +--R Type: Expression Integer +--E 80 + +--S 81 of 120 +ode87a:=solve(ode87,y,x) +--R +--R (78) "failed" +--R Type: Union("failed",...) +--E 81 + +--S 82 of 120 +ode88 := 2*D(y(x),x) - 3*y(x)**2 - 4*a*y(x) - b - c*exp(-2*a*x) +--R +--R , - 2a x 2 +--R (79) 2y (x) - c %e - 3y(x) - 4a y(x) - b +--R +--R Type: Expression Integer +--E 82 + +--S 83 of 120 +ode88a:=solve(ode88,y,x) +--R +--R (80) "failed" +--R Type: Union("failed",...) +--E 83 + +--S 84 of 120 +ode89 := x*D(y(x),x) - sqrt(a**2 - x**2) +--R +--R +---------+ +--R , | 2 2 +--R (81) xy (x) - \|- x + a +--R +--R Type: Expression Integer +--E 84 + +--S 85 of 120 +ode89a:=solve(ode89,y,x) +--R +--R (82) +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 2 \|- x + a - a 2 +--R (a\|- x + a - a )log(----------------) - x +--R x +--R [particular= ----------------------------------------------,basis= ] +--R +---------+ +--R | 2 2 +--R \|- x + a - a +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 85 + +--S 86 of 120 +yx:=ode89a.particular +--R +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 2 \|- x + a - a 2 +--R (a\|- x + a - a )log(----------------) - x +--R x +--R (83) ---------------------------------------------- +--R +---------+ +--R | 2 2 +--R \|- x + a - a +--R Type: Expression Integer +--E 86 + +--S 87 of 120 +ode89expr := x*D(yx,x) - sqrt(a**2 - x**2) +--R +--R (84) 0 +--R Type: Expression Integer +--E 87 + +--S 88 of 120 +ode90 := x*D(y(x),x) + y(x) - x*sin(x) +--R +--R , +--R (85) xy (x) - x sin(x) + y(x) +--R +--R Type: Expression Integer +--E 88 + +--S 89 of 120 +ode90a:=solve(ode90,y,x) +--R +--R sin(x) - x cos(x) 1 +--R (86) [particular= -----------------,basis= [-]] +--R x x +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 89 + +--S 90 of 120 +yx:=ode90a.particular +--R +--R sin(x) - x cos(x) +--R (87) ----------------- +--R x +--R Type: Expression Integer +--E 90 + +--S 91 of 120 +ode90expr := x*D(yx,x) + yx - x*sin(x) +--R +--R (88) 0 +--R Type: Expression Integer +--E 91 + +--S 92 of 120 +ode91 := x*D(y(x),x) - y(x) - x/log(x) +--R +--R , +--R x log(x)y (x) - y(x)log(x) - x +--R +--R (89) ------------------------------ +--R log(x) +--R Type: Expression Integer +--E 92 + +--S 93 of 120 +ode91a:=solve(ode91,y,x) +--R +--R (90) [particular= x log(log(x)),basis= [x]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 93 + +--S 94 of 120 +yx:=ode91a.particular +--R +--R (91) x log(log(x)) +--R Type: Expression Integer +--E 94 + +--S 95 of 120 +ode91expr := x*D(yx,x) - yx - x/log(x) +--R +--R (92) 0 +--R Type: Expression Integer +--E 95 + +--S 96 of 120 +ode92 := x*D(y(x),x) - y(x) - x**2*sin(x) +--R +--R , 2 +--R (93) xy (x) - x sin(x) - y(x) +--R +--R Type: Expression Integer +--E 96 + +--S 97 of 120 +ode92a:=solve(ode92,y,x) +--R +--R (94) [particular= - x cos(x),basis= [x]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 97 + +--S 98 of 120 +yx:=ode92a.particular +--R +--R (95) - x cos(x) +--R Type: Expression Integer +--E 98 + +--S 99 of 120 +ode92expr := x*D(yx,x) - yx - x**2*sin(x) +--R +--R (96) 0 +--R Type: Expression Integer +--E 99 + + +--S 100 of 120 +ode93 := x*D(y(x),x) - y(x) - x*cos(log(log(x)))/log(x) +--R +--R , +--R - x cos(log(log(x))) + x log(x)y (x) - y(x)log(x) +--R +--R (97) ------------------------------------------------- +--R log(x) +--R Type: Expression Integer +--E 100 + +--S 101 of 120 +ode93a:=solve(ode93,y,x) +--R +--R (98) [particular= x sin(log(log(x))),basis= [x]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 101 + +--S 102 of 120 +yx:=ode93a.particular +--R +--R (99) x sin(log(log(x))) +--R Type: Expression Integer +--E 102 + +--S 103 of 120 +ode93 := x*D(yx,x) - yx - x*cos(log(log(x)))/log(x) +--R +--R (100) 0 +--R Type: Expression Integer +--E 103 + +--S 104 of 120 +ode94 := x*D(y(x),x) +a*y(x) + b*x**n +--R +--R , n +--R (101) xy (x) + b x + a y(x) +--R +--R Type: Expression Integer +--E 104 + +--S 105 of 120 +ode94a:=solve(ode94,y,x) +--R +--R n log(x) +--R b %e - a log(x) +--R (102) [particular= - ------------,basis= [%e ]] +--R n + a +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 105 + +--S 106 of 120 +yx:=ode94a.particular +--R +--R n log(x) +--R b %e +--R (103) - ------------ +--R n + a +--R Type: Expression Integer +--E 106 + +--S 107 of 120 +ode94expr := x*D(yx,x) +a*yx + b*x**n +--R +--R n log(x) n +--R (104) - b %e + b x +--R Type: Expression Integer +--E 107 + +--S 108 of 120 +exprule := rule x^n == %e^(n*log(x)) +--R +--R n n log(x) +--R (105) x == %e +--R Type: RewriteRule(Integer,Integer,Expression Integer) +--E 108 + +--S 109 of 120 +exprule ode94expr +--R +--R (106) 0 +--R Type: Expression Integer +--E 109 + +--S 110 of 120 +ode95 := x*D(y(x),x) + y(x)**2 + x**2 +--R +--R , 2 2 +--R (107) xy (x) + y(x) + x +--R +--R Type: Expression Integer +--E 110 + +--S 111 of 120 +ode95a:=solve(ode95,y,x) +--R +--R +--R (108) "failed" +--R Type: Union("failed",...) +--E 111 + +--S 112 of 120 +ode96 := x*D(y(x),x) - y(x)**2 + 1 +--R +--R +--R , 2 +--R (109) xy (x) - y(x) + 1 +--R +--R Type: Expression Integer +--E 112 + +--S 113 of 120 +yx:=solve(ode96,y,x) +--R +--R - x y(x) - x +--R (110) ---------------------- +--R +--------+ +--------+ +--R \|y(x) - 1 \|y(x) + 1 +--R Type: Union(Expression Integer,...) +--E 113 + +--S 114 of 120 +ode96expr := x*D(yx,x) - yx**2 + 1 +--R +--R (111) +--R 2 , 2 2 +--------+ +--------+ 2 +--R x y (x) + ((- x + 1)y(x) - x - 1)\|y(x) - 1 \|y(x) + 1 - x y(x) + x +--R +--R ----------------------------------------------------------------------- +--R +--------+ +--------+ +--R (y(x) - 1)\|y(x) - 1 \|y(x) + 1 +--R Type: Expression Integer +--E 114 + +--S 115 of 120 +ode98 := x*D(y(x),x) + a*y(x)**2 - b*y(x) + c*x**(2*b) +--R +--R +--R , 2b 2 +--R (112) xy (x) + c x + a y(x) - b y(x) +--R +--R Type: Expression Integer +--E 115 + +--S 116 of 120 +ode98a:=solve(ode98,y,x) +--R +--R (113) "failed" +--R Type: Union("failed",...) +--E 116 + +--S 117 of 120 +ode99 := x*D(y(x),x) + a*y(x)**2 - b*y(x) - c*x**beta +--R +--R +--R , beta 2 +--R (114) xy (x) - c x + a y(x) - b y(x) +--R +--R Type: Expression Integer +--E 117 + +--S 118 of 120 +ode99a:=solve(ode99,y,x) +--R +--R +--R (115) "failed" +--R Type: Union("failed",...) +--E 118 + +--S 119 of 120 +ode100 := x*D(y(x),x) + x*y(x)**2 + a +--R +--R +--R , 2 +--R (116) xy (x) + x y(x) + a +--R +--R Type: Expression Integer +--E 119 + +--S 120 of 120 +ode100a:=solve(ode100,y,x) +--R +--R +--R (117) "failed" +--R Type: Union("failed",...) +--E 120 +)spool +)lisp (bye) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} {\bf http://www.cs.uwaterloo.ca/$\tilde{}$ecterrab/odetools.html} +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/kamke1.input.pdf b/src/axiom-website/CATS/kamke1.input.pdf new file mode 100644 index 0000000..1a1b835 Binary files /dev/null and b/src/axiom-website/CATS/kamke1.input.pdf differ diff --git a/src/axiom-website/CATS/kamke2.input.pamphlet b/src/axiom-website/CATS/kamke2.input.pamphlet new file mode 100644 index 0000000..b4c8b85 --- /dev/null +++ b/src/axiom-website/CATS/kamke2.input.pamphlet @@ -0,0 +1,2217 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input kamke2.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This is the 50 ODEs of the Kamke test suite as published by +E. S. Cheb-Terrab\cite{1}. They have been rewritten using Axiom +syntax. Where possible we show that the particular solution actually +satisfies the original ordinary differential equation. +\end{abstract} +\eject +\tableofcontents +\eject +<<*>>= +)spool kamke2.output +)set break resume +)set mes auto off +)clear all + +--S 1 of 126 +y:=operator 'y +--R +--R (1) y +--R Type: BasicOperator +--E 1 + +--S 2 of 126 +f:=operator 'f +--R +--R (2) f +--R Type: BasicOperator +--E 2 + +--S 3 of 126 +g:=operator 'g +--R +--R (3) g +--R Type: BasicOperator +--E 3 + +------------------------------------------------------------------- +--S 4 of 126 +ode101 := x*D(y(x),x) + x*y(x)**2 - y(x) +--R +--R , 2 +--R (4) xy (x) + x y(x) - y(x) +--R +--R Type: Expression Integer +--E 4 + +@ +Maxima gives $$\frac{2x}{x^2-2\%c}$$ +which can be substituted and simplifies to 0. + +Maple gives +$$\frac{2x}{x^2+2\_C1}$$ +which can be substituted and simplifies to 0. + +Mathematica gives +$$y(x)=\frac{2x}{x^2+2}$$ +which can be substituted and simplifies to 0. +<<*>>= +--S 5 of 126 +yx:=solve(ode101,y,x) +--R +--R 2 +--R x y(x) - 2x +--R (5) ----------- +--R 2y(x) +--R Type: Union(Expression Integer,...) +--E 5 + +--S 6 of 126 +ode101expr := x*D(yx,x) + x*yx**2 - yx +--R +--R 2 , 5 2 2 4 3 +--R 4x y (x) + (x + 2x )y(x) - 4x y(x) + 4x +--R +--R (6) ------------------------------------------ +--R 2 +--R 4y(x) +--R Type: Expression Integer +--E 6 + +------------------------------------------------------------------- +--S 7 of 126 +ode102 := x*D(y(x),x) + x*y(x)**2 - y(x) - a*x**3 +--R +--R , 2 3 +--R (7) xy (x) + x y(x) - y(x) - a x +--R +--R Type: Expression Integer +--E 7 + +@ +Maxima fails. + +Maple gives +$$\tanh(\left(\frac{x^2\sqrt{a}}{2}+\_C1\sqrt{a}\right)x\sqrt{a}$$ +which, upon substitution, simplifies to 0. + +Mathematica gives +$$\sqrt{a}~x~ +\tanh\left(\frac{1}{2}\left(\sqrt{a}~x^2+2\sqrt{a}~C\right)\right)$$ +which, upon substitution, cannot be simplified to 0. +<<*>>= +--S 8 of 126 +yx:=solve(ode102,y,x) +--R +--R +-+ +--R (2y(x) + 3x)\|a + 3y(x) + 2a x +--R (8) --------------------------------------------- +--R 2 +-+ +--R +-+ x \|a +--R ((6y(x) - 4a x)\|a + 4a y(x) - 6a x)%e +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 126 +ode102expr := x*D(yx,x) + x*yx**2 - yx - a*x**3 +--R +--R (9) +--R 2 2 3 2 3 +-+ +--R ((- 144a - 108a)x y(x) + (32a + 216a )x )\|a +--R + +--R 3 2 2 3 2 3 +--R (- 32a - 216a )x y(x) + (144a + 108a )x +--R * +--R 2 +-+ +--R x \|a , +--R %e y (x) +--R +--R + +--R 3 2 3 3 4 3 4 2 +--R (- 144a - 108a )x y(x) + (96a + 648a )x y(x) +--R + +--R 4 3 5 5 4 6 +--R (- 432a - 324a )x y(x) + (32a + 216a )x +--R * +--R +-+ +--R \|a +--R + +--R 4 3 3 3 4 3 4 2 +--R (- 32a - 216a )x y(x) + (432a + 324a )x y(x) +--R + +--R 5 4 5 5 4 6 +--R (- 96a - 648a )x y(x) + (144a + 108a )x +--R * +--R 2 +-+ 2 +--R x \|a +--R (%e ) +--R + +--R 2 2 2 3 +--R ((- 144a - 108a)x - 16a - 108a)y(x) +--R + +--R 3 2 3 2 2 +--R ((32a + 216a )x + (216a + 162a)x)y(x) +--R + +--R 3 2 4 3 2 2 4 3 5 +--R ((144a + 108a )x + (- 16a - 108a )x )y(x) + (- 32a - 216a )x +--R + +--R 3 2 3 +--R (- 72a - 54a )x +--R * +--R +-+ +--R \|a +--R + +--R 3 2 2 2 3 +--R ((- 32a - 216a )x - 72a - 54a)y(x) +--R + +--R 3 2 3 3 2 2 +--R ((144a + 108a )x + (48a + 324a )x)y(x) +--R + +--R 4 3 4 3 2 2 4 3 5 +--R ((32a + 216a )x + (- 72a - 54a )x )y(x) + (- 144a - 108a )x +--R + +--R 4 3 3 +--R (- 16a - 108a )x +--R * +--R 2 +-+ +--R x \|a +--R %e +--R + +--R 3 2 2 2 2 3 +--R (36a + 27)x y(x) + (8a + 54a)x y(x) + (- 36a - 27a)x y(x) +--R + +--R 3 2 4 +--R (- 8a - 54a )x +--R * +--R +-+ +--R \|a +--R + +--R 2 3 2 2 2 3 2 3 +--R (8a + 54a)x y(x) + (36a + 27a)x y(x) + (- 8a - 54a )x y(x) +--R + +--R 3 2 4 +--R (- 36a - 27a )x +--R / +--R 2 3 3 2 2 +--R (144a + 108a)y(x) + (- 96a - 648a )x y(x) +--R + +--R 3 2 2 4 3 3 +--R (432a + 324a )x y(x) + (- 32a - 216a )x +--R * +--R +-+ +--R \|a +--R + +--R 3 2 3 3 2 2 4 3 2 +--R (32a + 216a )y(x) + (- 432a - 324a )x y(x) + (96a + 648a )x y(x) +--R + +--R 4 3 3 +--R (- 144a - 108a )x +--R * +--R 2 +-+ 2 +--R x \|a +--R (%e ) +--R Type: Expression Integer +--E 9 + +------------------------------------------------------------------- +--S 10 of 126 +ode103 := x*D(y(x),x) + x*y(x)**2 - (2*x**2+1)*y(x) - x**3 +--R +--R , 2 2 3 +--R (10) xy (x) + x y(x) + (- 2x - 1)y(x) - x +--R +--R Type: Expression Integer +--E 10 + +@ +Maxima fails. + +Maple gives +$$\frac{1}{2}x\left(\sqrt{2}+ +2\tanh\left(\frac{(x^2+x\_C1)\sqrt{2}}{2}\right)\right)\sqrt{2}$$ +which simplifies to 0 on substitution. + +Mathematica gives +$$\frac{\left(e^{\sqrt{x}~x^2}+\sqrt{2}~e^{\sqrt{2}~x^2}+ +e^{2\sqrt{2}~C}-\sqrt{2}~e^{2\sqrt{2}~C}\right)x} +{e^{\sqrt{2}~x^2}+e^{2*\sqrt{2}~C}}$$ +which does not simplify to 0 on substitution. +<<*>>= +--S 11 of 126 +yx:=solve(ode103,y,x) +--R +--R +-+ +-+ +--R (2\|2 + 3)y(x) + x\|2 + x +--R (11) ----------------------------------------- +--R 2 +-+ +--R +-+ +-+ x \|2 +--R ((6\|2 + 8)y(x) - 14x\|2 - 20x)%e +--R Type: Union(Expression Integer,...) +--E 11 + +--S 12 of 126 +ode103expr := x*D(yx,x) + x*yx**2 - (2*x**2+1)*yx - x**3 +--R +--R (12) +--R 2 +-+ +--R 2 +-+ 2 3 +-+ 3 x \|2 , +--R ((- 792x \|2 - 1120x )y(x) + 1912x \|2 + 2704x )%e y (x) +--R +--R + +--R 3 +-+ 3 3 4 +-+ 4 2 +--R (- 792x \|2 - 1120x )y(x) + (5736x \|2 + 8112x )y(x) +--R + +--R 5 +-+ 5 6 +-+ 6 +--R (- 13848x \|2 - 19584x )y(x) + 11144x \|2 + 15760x +--R * +--R 2 +-+ 2 +--R x \|2 +--R (%e ) +--R + +--R 2 +-+ 2 3 +--R ((- 1352x - 280)\|2 - 1912x - 396)y(x) +--R + +--R 3 +-+ 3 2 +--R ((5968x + 2028x)\|2 + 8440x + 2868x)y(x) +--R + +--R 4 2 +-+ 4 2 +--R ((- 5176x - 2984x )\|2 - 7320x - 4220x )y(x) +--R + +--R 5 3 +-+ 5 3 +--R (- 3264x - 676x )\|2 - 4616x - 956x +--R * +--R 2 +-+ +--R x \|2 +--R %e +--R + +--R +-+ 3 2 +-+ 2 2 +--R (99x\|2 + 140x)y(x) + (- 157x \|2 - 222x )y(x) +--R + +--R 3 +-+ 3 4 +-+ 4 +--R (- 181x \|2 - 256x )y(x) - 41x \|2 - 58x +--R / +--R +-+ 3 +-+ 2 +--R (792\|2 + 1120)y(x) + (- 5736x\|2 - 8112x)y(x) +--R + +--R 2 +-+ 2 3 +-+ 3 +--R (13848x \|2 + 19584x )y(x) - 11144x \|2 - 15760x +--R * +--R 2 +-+ 2 +--R x \|2 +--R (%e ) +--R Type: Expression Integer +--E 12 + +------------------------------------------------------------------- +--S 13 of 126 +ode106 := x*D(y(x),x) + x**a*y(x)**2 + (a-b)*y(x)/2 + x**b +--R +--R , b 2 a +--R 2xy (x) + 2x + 2y(x) x + (- b + a)y(x) +--R +--R (13) ---------------------------------------- +--R 2 +--R Type: Expression Integer +--E 13 + +@ +Maxima fails. + +Maple gets +$$-\frac{\tan\left( +\frac2x^{\left(\displaystyle +\frac{a}{2}+\frac{b}{2}\right)}+\displaystyle\_C1~a+\_C1~b} +a+b}\right)} +{x^{\left(\displaystyle{\frac{a}{2}-\displaystyle\frac{b}{2}}\right)}$$ +which simplifies to 0 on substitution. + + +Mathematica gets +$$e^{-\frac{1}{2}a\log(x)+\frac{1}{2}b\log(x)} +\tan\left(\frac{2x^{\frac{a+b}{2}}}{a+b}-C\right)$$ +which does not simplify to 0 on substitution. +<<*>>= +--S 14 of 126 +yx:=solve(ode106,y,x) +--R +--R (14) "failed" +--R Type: Union("failed",...) +--E 14 + +------------------------------------------------------------------- +--S 15 of 126 +ode107 := x*D(y(x),x) + a*x**alpha*y(x)**2 + b*y(x) - c*x**beta +--R +--R , beta 2 alpha +--R (15) xy (x) - c x + a y(x) x + b y(x) +--R +--R Type: Expression Integer +--E 15 + +@ +Maxima fails. +<<*>>= +--S 16 of 126 +yx:=solve(ode107,y,x) +--R +--R (16) "failed" +--R Type: Union("failed",...) +--E 16 + +------------------------------------------------------------------- +--S 17 of 126 +ode108 := x*D(y(x),x) - y(x)**2*log(x) + y(x) +--R +--R , 2 +--R (17) xy (x) - y(x) log(x) + y(x) +--R +--R Type: Expression Integer +--E 17 +@ +Maxima gets: +$$\frac{1}{x\left(\frac{\log(x)}{x}+\frac{1}{x}+\%c\right)}$$ +which does not simplify on substitution. + +Maple gets: +$$\frac{1}{1+\log(x)+x\_C1}$$ +which, on substitution, simplifies to 0. + +Mathematica gets: +$$\frac{1}{1+xC+\log(x)}$$ +which, on substitution, simplifies to 0. +<<*>>= +--S 18 of 126 +yx:=solve(ode108,y,x) +--R +--R - y(x)log(x) - y(x) + 1 +--R (18) ----------------------- +--R x y(x) +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 126 +ode108expr := x*D(yx,x) - yx**2*log(x) + yx +--R +--R (19) +--R 2 , 2 3 2 2 +--R - x y (x) - y(x) log(x) + (- 2y(x) + 2y(x))log(x) +--R +--R + +--R 2 2 +--R (- y(x) + 2y(x) - 1)log(x) - x y(x) +--R / +--R 2 2 +--R x y(x) +--R Type: Expression Integer +--E 19 + +------------------------------------------------------------------- +--S 20 of 126 +ode109 := x*D(y(x),x) - y(x)*(2*y(x)*log(x)-1) +--R +--R , 2 +--R (20) xy (x) - 2y(x) log(x) + y(x) +--R +--R Type: Expression Integer +--E 20 + +@ +Maxima gets: +$$\frac{1}{x\left(\%c-2\left(-\frac{\log(x)}{x}-\frac{1}{x}\right)\right)}$$ +which does not simplify to 0 on substitution. + +Maple gets: +$$\frac{1}{2+2\log(x)+x~\_C1}$$ +which simplifies to 0 on substitition. + +Mathematica gets +$$\frac{1}{2+xC+2\log(x)}$$ +which simplifies to 0 on substitution. +<<*>>= +--S 21 of 126 +yx:=solve(ode109,y,x) +--R +--R - 2y(x)log(x) - 2y(x) + 1 +--R (21) ------------------------- +--R x y(x) +--R Type: Union(Expression Integer,...) +--E 21 + +--S 22 of 126 +ode109expr := x*D(yx,x) - yx*(2*yx*log(x)-1) +--R +--R (22) +--R 2 , 2 3 2 2 +--R - x y (x) - 8y(x) log(x) + (- 16y(x) + 8y(x))log(x) +--R +--R + +--R 2 2 +--R (- 8y(x) + 8y(x) - 2)log(x) - 2x y(x) +--R / +--R 2 2 +--R x y(x) +--R Type: Expression Integer +--E 22 + +------------------------------------------------------------------- +--S 23 of 126 +ode110 := x*D(y(x),x) + f(x)*(y(x)**2-x**2) +--R +--R , 2 2 +--R (23) xy (x) + f(x)y(x) - x f(x) +--R +--R Type: Expression Integer +--E 23 + +@ +Maxima failed. +<<*>>= +--S 24 of 126 +yx:=solve(ode110,y,x) +--R +--R (24) "failed" +--R Type: Union("failed",...) +--E 24 + +------------------------------------------------------------------- +--S 25 of 126 +ode111 := x*D(y(x),x) + y(x)**3 + 3*x*y(x)**2 +--R +--R , 3 2 +--R (25) xy (x) + y(x) + 3x y(x) +--R +--R Type: Expression Integer +--E 25 + +@ +Maxima fails. + +Maple gets 0 which simplifies to 0 on substitution. +<<*>>= + +--S 26 of 126 +yx:=solve(ode111,y,x) +--R +--R (26) "failed" +--R Type: Union("failed",...) +--E 26 + +------------------------------------------------------------------- +--S 27 of 126 +ode112 := x*D(y(x),x) - sqrt(y(x)**2 + x**2) - y(x) +--R +--R +----------+ +--R , | 2 2 +--R (27) xy (x) - \|y(x) + x - y(x) +--R +--R Type: Expression Integer +--E 27 + +@ +Maxima gets +$$x=\%c \%e^+\frac{x {\rm asinh}\left(\frac{y}{x}\right)}{\vert x\vert}$$ +which does not simplify to 0 on substitution. + +Maple gets 0 but simplification gives the result $csgn(x)x$. +<<*>>= + +--S 28 of 126 +yx:=solve(ode112,y,x) +--R +--R (28) "failed" +--R Type: Union("failed",...) +--E 28 + +------------------------------------------------------------------- +--S 29 of 126 +ode113 := x*D(y(x),x) + a*sqrt(y(x)**2 + x**2) - y(x) +--R +--R +----------+ +--R , | 2 2 +--R (29) xy (x) + a\|y(x) + x - y(x) +--R +--R Type: Expression Integer +--E 29 + +@ +Maxima gets +$$x=\%c \%e^+-\frac{x {\rm asinh}\left(\frac{y}{x}\right)}{a\vert x\vert}$$ +which does not simplify to 0 on substitution. + +Maple gets 0 but on substitition this simplifies to $a~csgn(x)~x$ + +Mathematica gets +$$x*\sinh(C+\log(x))$$ +If we choose $C=0$ this simplifies to +$$\frac{1}{2}(-1+x^2)$$ +However, Mathematica cannot simplify either substition to 0. +<<*>>= +--S 30 of 126 +yx:=solve(ode113,y,x) +--R +--R (30) "failed" +--R Type: Union("failed",...) +--E 30 + +------------------------------------------------------------------- +--S 31 of 126 +ode114 := x*D(y(x),x) - x*sqrt(y(x)**2 + x**2) - y(x) +--R +--R +----------+ +--R , | 2 2 +--R (31) xy (x) - x\|y(x) + x - y(x) +--R +--R Type: Expression Integer +--E 31 + +@ +Maxima fails. + +Maple gets 0 but, on substitition, simplifies to $-x^2csqn(x)$. + +Mathematica gets +$$x\sinh(x+C)$$ +but cannot simplify the substituted expression to 0. +<<*>>= +--S 32 of 126 +yx:=solve(ode114,y,x) +--R +--R (32) "failed" +--R Type: Union("failed",...) +--E 32 + +------------------------------------------------------------------- +--S 33 of 126 +ode115 := x*D(y(x),x) - x*(y(x)-x)*sqrt(y(x)**2 + x**2) - y(x) +--R +--R +----------+ +--R , 2 | 2 2 +--R (33) xy (x) + (- x y(x) + x )\|y(x) + x - y(x) +--R +--R Type: Expression Integer +--E 33 + +@ +Maxima failed. + +Maple claims the result is 0 but simplifies it, on substitution, to +$x^3 csgn(x)$. + +Mathematica claims that the equations appear to involve the variables +to be solved for in an essentially non-algebraic way. +<<*>>= +--S 34 of 126 +yx:=solve(ode115,y,x) +--R +--R (34) "failed" +--R Type: Union("failed",...) +--E 34 + +------------------------------------------------------------------- +--S 35 of 126 +ode116 := x*D(y(x),x) - x*sqrt((y(x)**2 - x**2)*(y(x)**2-4*x**2)) - y(x) +--R +--R +----------------------+ +--R , | 4 2 2 4 +--R (35) xy (x) - x\|y(x) - 5x y(x) + 4x - y(x) +--R +--R Type: Expression Integer +--E 35 + +@ +Maxima failed. + +Maple claims the answer is 0 but simplifies, on substitution, to +$-2x^3 csgn(x^2)$. + +Mathematica says that a potential solution of ComplexInfinity was possibly +discarded by the verifier and should be checked by hand, possibly using +limits. And the equations appear to involve the variables to be solved +for in an essentially non-algebraic way. +<<*>>= +--S 36 of 126 +yx:=solve(ode116,y,x) +--R +--R (36) "failed" +--R Type: Union("failed",...) +--E 36 + +------------------------------------------------------------------- +--S 37 of 126 +ode117 := x*D(y(x),x) - x*exp(y(x)/x) - y(x) - x +--R +--R y(x) +--R ---- +--R , x +--R (37) xy (x) - x %e - y(x) - x +--R +--R Type: Expression Integer +--E 37 + +@ +Maxima gets: +$$\%c~x=\%e^-\frac{x\log(\%e^{y/x}+1)-y}{x}$$ +which does not simplify to 0 on substitution. + +Maple gets: +$$\left(\log\left(-\frac{x}{-1+x~e^{\_C1}}\right)+\_C1\right)x$$ +which simplifies to 0 on substitution. + +Mathematica says that inverse functions are being used by Solve, so some +solutions may not be found and to use Reduce for complete solution +information. It gets the answer: +$$-x\log\left(-1+\frac{e^{-C}}{x}\right)$$ +which simplifies to 0. +<<*>>= +--S 38 of 126 +yx:=solve(ode117,y,x) +--R +--R (38) "failed" +--R Type: Union("failed",...) +--E 38 + +------------------------------------------------------------------- +--S 39 of 126 +ode118 := x*D(y(x),x) - y(x)*log(y(x)) +--R +--R , +--R (39) xy (x) - y(x)log(y(x)) +--R +--R Type: Expression Integer +--E 39 + +@ +Maxima gets +$$\%e^{\%e^{\%c}x}$$ +which, on substitution, simplifies to 0. + +Maple gets +$$e^{(x~\_C1)}$$ +which, on substitution, does not simplify to 0. + +Mathematics gets +$$e^{e^{C}x}$$ +which, on substitution simplifies to +$$e^x(x-\log(e^x))$$ which, if $log(e^x)$ could simplify to $x$ +then the result would be 0. +<<*>>= +--S 40 of 126 +yx:=solve(ode118,y,x) +--R +--R x +--R (40) - --------- +--R log(y(x)) +--R Type: Union(Expression Integer,...) +--E 40 + +--S 41 of 126 +ode118expr := x*D(yx,x) - yx*log(yx) +--R +--R x 2 , +--R x y(x)log(y(x))log(- ---------) + x y (x) - x y(x)log(y(x)) +--R log(y(x)) +--R (41) ----------------------------------------------------------- +--R 2 +--R y(x)log(y(x)) +--R Type: Expression Integer +--E 41 + +------------------------------------------------------------------- +--S 42 of 126 +ode119 := x*D(y(x),x) - y(x)*(log(x*y(x))-1) +--R +--R , +--R (42) xy (x) - y(x)log(x y(x)) + y(x) +--R +--R Type: Expression Integer +--E 42 + +@ +$$\frac{1}{x}$$ simplifies to 0. + +Maxima gets +$$\frac{\%e^{x/\%c}}{x}$$ +which, on substitution, does not simplify to 0. + +Maple get +$$\frac{e^{\left(\frac{x}{\_C1}\right)}}{x}$$ +which, on substitution, does not simplify to 0. + +Mathematica gets +$$\frac{1}{x(C-log(log(x)))}$$ +which does not simplify to 0 on substitution. +<<*>>= +--S 43 of 126 +yx:=solve(ode119,y,x) +--R +--R (43) "failed" +--R Type: Union("failed",...) +--E 43 + +------------------------------------------------------------------- +--S 44 of 126 +ode120 := x*D(y(x),x) - y(x)*(x*log(x**2/y(x))+2) +--R +--R 2 +--R , x +--R (44) xy (x) - x y(x)log(----) - 2y(x) +--R y(x) +--R Type: Expression Integer +--E 44 + +@ +Maxima fails. + +Maple gets +$$\frac{x^2}{e^{\left(\frac{\_C1}{e^x}\right)}}$$ +which, on substitution, does not simplify to 0. + +Mathematics get: +$$2e^{-e^{-x} C+e^{-x}{\rm ExpIntegralEi}[x]}x$$ +which does not simplify to 0 on substitution. +<<*>>= +--S 45 of 126 +yx:=solve(ode120,y,x) +--R +--R (45) "failed" +--R Type: Union("failed",...) +--E 45 + +------------------------------------------------------------------- +--S 46 of 126 +ode121 := x*D(y(x),x) + sin(y(x)-x) +--R +--R , +--R (46) xy (x) + sin(y(x) - x) +--R +--R Type: Expression Integer +--E 46 + +@ +Maxima fails. + +Mathematics gets +$$\frac{\sin(x)}{1+\sin(x)}+x^{-sin(x)}C$$ +which, on substitution, does not simplify to 0. +<<*>>= +--S 47 of 126 +yx:=solve(ode121,y,x) +--R +--R (47) "failed" +--R Type: Union("failed",...) +--E 47 + +------------------------------------------------------------------- +--S 48 of 126 +ode122 := x*D(y(x),x) + (sin(y(x))-3*x**2*cos(y(x)))*cos(y(x)) +--R +--R , 2 2 +--R (48) xy (x) + cos(y(x))sin(y(x)) - 3x cos(y(x)) +--R +--R Type: Expression Integer +--E 48 + +@ +Maxima fails. + +Maple gets: +$$\arctan\left(\frac{x^3+2~\_C1}{x}\right)$$ +which, on substitution, simplifies to 0. + +Mathematica gets: +$$\arctan\left(\frac{2x^3+C}{2x}\right)$$ +which, on substitution, simplifies to 0. +<<*>>= +--S 49 of 126 +yx:=solve(ode122,y,x) +--R +--R (49) "failed" +--R Type: Union("failed",...) +--E 49 + +------------------------------------------------------------------- +--S 50 of 126 +ode123 := x*D(y(x),x) - x*sin(y(x)/x) - y(x) +--R +--R , y(x) +--R (50) xy (x) - x sin(----) - y(x) +--R x +--R Type: Expression Integer +--E 50 + +@ +Maxima gets: +$$\%c~x=\%e^-\frac{ +\log\left(\cos\left(\frac{y}{x}\right)+1\right)- +\log\left(\cos\left(\frac{y}{x}\right)-1\right)}{2}$$ +which, on substitution, does not simplify to 0. + +Maple gets: +$$\arctan\left(\frac{2x~\_C1}{1+x^2~\_C1^2}\quad,\quad +-\frac{-1+x^2~\_C1^2}{1+x^2~\_C1^2}\right)x$$ +which, on substitution, simplifies to 0. + +Mathematica get: +$$x^{1+sin(x)}C$$ +which does not simplfy to 0 on substitution. +<<*>>= +--S 51 of 126 +yx:=solve(ode123,y,x) +--R +--R (51) "failed" +--R Type: Union("failed",...) +--E 51 + +------------------------------------------------------------------- +--S 52 of 126 +ode124 := x*D(y(x),x) + x*cos(y(x)/x) - y(x) + x +--R +--R , y(x) +--R (52) xy (x) + x cos(----) - y(x) + x +--R x +--R Type: Expression Integer +--E 52 + +@ +Maxima gets: +$$\%c~x=\%e^-\frac{\sin\left(\frac{y}{x}\right)} +{\cos\left(\frac{y}{x}\right)+1}$$ +which, on substitution, does not simplify to 0. + +Maple gets +$$-2\arctan(\log(x)+~\_C1)x$$ +which, on substitution, does not simplify to 0. + +Mathematics gets +$$2x\arctan(C-\log(x))$$ +which does not simplify to 0 on substitution. +<<*>>= +--S 53 of 126 +yx:=solve(ode124,y,x) +--R +--R (53) "failed" +--R Type: Union("failed",...) +--E 53 + +------------------------------------------------------------------- +--S 54 of 126 +ode125 := x*D(y(x),x) + x*tan(y(x)/x) - y(x) +--R +--R , y(x) +--R (54) xy (x) + x tan(----) - y(x) +--R x +--R Type: Expression Integer +--E 54 + +@ +Maxima gets: +$$\arcsin\left(\frac{1}{\%c~x}\right)x$$ +which, on substitition, does simplifes to 0. + +Maple gets +$$\arcsin\left(\frac{1}{x~\_C1}\right)x$$ +which, on substitution, simplifies to 0. + +Mathematica gets +$$\arcsin\left(\frac{e^{C}}{x}\right)$$ +which does not simplify to 0 on substitution. +<<*>>= +--S 55 of 126 +yx:=solve(ode125,y,x) +--R +--R (55) "failed" +--R Type: Union("failed",...) +--E 55 + +------------------------------------------------------------------- +--S 56 of 126 +ode126 := x*D(y(x),x) - y(x)*f(x*y(x)) +--R +--R , +--R (56) xy (x) - y(x)f(x y(x)) +--R +--R Type: Expression Integer +--E 56 + +@ +Maxima fails. + +Maple gets +$$\frac{{\rm RootOf}\left(-\log(x)+~\_C1+ +\displaystyle\int^{\_Z}{\frac{1}{\displaystyle\_a(1+g(\_a))}}~d\_a\right)}{x}$$ +which, on substitution, simplifies to 0. + +Mathematica gets +$$\frac{1}{-f(x)-C}$$ +which does not simplify to 0 on substitution. +<<*>>= +--S 57 of 126 +yx:=solve(ode126,y,x) +--R +--R (57) "failed" +--R Type: Union("failed",...) +--E 57 + +------------------------------------------------------------------- +--S 58 of 126 +ode127 := x*D(y(x),x) - y(x)*f(x**a*y(x)**b) +--R +--R a b , +--R (58) - y(x)f(x y(x) ) + xy (x) +--R +--R Type: Expression Integer +--E 58 +@ +Maxima fails. + +Maple gives 0 which, on substitution simplifies to 0. + +Mathematica gives: +$$b\left(-\frac{f(x^a)}{a}-C\right)^{-1/b}$$ +which, on substitution, does not simplify to 0. +<<*>>= +--S 59 of 126 +yx:=solve(ode127,y,x) +--R +--R (59) "failed" +--R Type: Union("failed",...) +--E 59 + +------------------------------------------------------------------- +--S 60 of 126 +ode128 := x*D(y(x),x) + a*y(x) - f(x)*g(x**a*y(x)) +--R +--R , a +--R (60) xy (x) - f(x)g(y(x)x ) + a y(x) +--R +--R Type: Expression Integer +--E 60 +@ +Maxima fails. + +Maple gives +$$\frac{{\rm RootOf}\left( +-\int{f(x)x^{(-1+a)}}~dx+\int^{\_Z}{\frac{1}{g(\_a)}~d\_a+\_C1}\right)}{x^a}$$ +which, on substitution, gives 0. + +Mathematica gives +$$e^{\frac{f(x)g(x^{1+a})}{1+a}-a\log(x)}C$$ +which, on substitution, does not simplify to 0. +<<*>>= +--S 61 of 126 +yx:=solve(ode128,y,x) +--R +--R (61) "failed" +--R Type: Union("failed",...) +--E 61 + +------------------------------------------------------------------- +--S 62 of 126 +ode129 := (x+1)*D(y(x),x) + y(x)*(y(x)-x) +--R +--R , 2 +--R (62) (x + 1)y (x) + y(x) - x y(x) +--R +--R Type: Expression Integer +--E 62 +@ +Maxima gets: +$$\frac{\%e^x}{(x+1)\left(\int{\frac{\%e^x}{(x+1)^2}}~dx+\%c\right)}$$ +which, on substitution, does not simplify to 0. + +Maple gives +$$\frac{e^x} +{-e^x-e^{(-1)}{\rm Ei}(1,-x-1)x-e^{(-1)}{\rm Ei}(1,-x-1)+x~\_C1+~\_C1}$$ +which, on substitution, simplifies to 0. + +Mathematica gives +$$-\frac{e^{1+x}}{e^{1+x}-eC-exC-{\rm ExpIntegralEi}(1+x)- +x{\rm ExpIntegralEi}(1+x)}$$ +<<*>>= +--S 63 of 126 +yx:=solve(ode129,y,x) +--R +--R +--R x +--R - x ++ 1 +--I (- x - 1)y(x)%e | --------------------- d%U + 1 +--I ++ 2 - %U +--I (%U + 2%U + 1)%e +--R (63) ----------------------------------------------------- +--R - x +--R (x + 1)y(x)%e +--R Type: Union(Expression Integer,...) +--E 63 + +------------------------------------------------------------------- +--S 64 of 126 +ode130 := 2*x*D(y(x),x) - y(x) -2*x**3 +--R +--R , 3 +--R (64) 2xy (x) - y(x) - 2x +--R +--R Type: Expression Integer +--E 64 +@ +Maxima gets: +$$\%e^{\displaystyle\frac{\log(x)}{2}}\displaystyle +\left(\frac{2\%e^{\displaystyle\frac{5\log(x)}{2}}}{5}+\%c\right)$$ +which, on substitution, does not give 0. + +Maple gives +$$\frac{2x^3}{5}+\sqrt{x}~\_C1$$ +which, on substitution, simplifies to 0. + +Mathematica gives +$$\frac{2x^3}{5}+\sqrt{x}C$$ +which simplifies to 0 on substitution. +<<*>>= +--S 65 of 126 +ode130a:=solve(ode130,y,x) +--R +--R 3 +--R 2x +-+ +--R (65) [particular= ---,basis= [\|x ]] +--R 5 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 65 + +--S 66 of 126 +yx:=ode130a.particular +--R +--R 3 +--R 2x +--R (66) --- +--R 5 +--R Type: Expression Integer +--E 66 + +--S 67 of 126 +ode130expr := 2*x*D(yx,x) - yx -2*x**3 +--R +--R (67) 0 +--R Type: Expression Integer +--E 67 + +------------------------------------------------------------------- +--S 68 of 126 +ode131 := (2*x+1)*D(y(x),x) - 4*exp(-y(x)) + 2 +--R +--R , - y(x) +--R (68) (2x + 1)y (x) - 4%e + 2 +--R +--R Type: Expression Integer +--E 68 +@ +Maxima gets: +$$\log\left(\frac{4\%e^{2\%c}x+2\%e^{2\%c}+1} +{2\%e^{2\%c}x+\%e^{2\%c}}\right)$$ +which simplifies to 0 when substituted. + +Maple gives +$$-\log\left(\frac{2x+1}{-1+4xe^{(2~\_C1)}+2e^{(2~\_C1)}}\right)-2~\_C1$$ +which simplifies to 0 when substituted. + +Mathematica gives +$$\log\left(2+\frac{1}{1+2x}\right)$$ +which simplifies to 0 when substituted. +<<*>>= +--S 69 of 126 +yx:=solve(ode131,y,x) +--R +--R - y(x) y(x) +--R (69) (- 4x %e + 2x + 1)%e +--R Type: Union(Expression Integer,...) +--E 69 + +--S 70 of 126 +ode131expr := (2*x+1)*D(yx,x) - 4*exp(-yx) + 2 +--R +--R (70) +--R - y(x) y(x) +--R (4x %e - 2x - 1)%e 2 y(x) , +--R - 4%e + (4x + 4x + 1)%e y (x) +--R +--R + +--R - y(x) y(x) +--R ((- 8x - 4)%e + 4x + 2)%e + 2 +--R Type: Expression Integer +--E 70 + +------------------------------------------------------------------- +--S 71 of 126 +ode132 := 3*x*D(y(x),x) - 3*x*log(x)*y(x)**4 - y(x) +--R +--R , 4 +--R (71) 3xy (x) - 3x y(x) log(x) - y(x) +--R +--R Type: Expression Integer +--E 71 +@ +Maxima gives 3 solutions. +$$-\frac{\left(\sqrt{3}~4^{1/3}\%i-4^{1/3}\right)x^{1/3}} +{2\left(6x^2\log(x)-3x^2+4\%c\right)^{1/3}}$$ +$$\frac{\left(\sqrt{3}~4^{1/3}\%i+4^{1/3}\right)x^{1/3}} +{2\left(6x^2\log(x)-3x^2+4\%c\right)^{1/3}}$$ +$$-\frac{4^{1/3}x^{1/3}}{\left(6x^2\log(x)-3x^2+4\%c\right)^{1/3}}$$ +which, on substitution, simplifies to 0. + + +Maple gives 3 solutions. +$$\frac{\left(-4x(6x^2\log(x)-3x^2-4~\_C1)^2\right)^{(1/3)}} +{6x^2\log(x)-3*x^2-4~\_C1}$$ +$$-\frac{1}{2}\frac{\left(-4x(6x^2\log(x)-3x^2-4~\_C1)^2\right)^{(1/3)}} +{6x^2\log(x)-3*x^2-4~\_C1} ++\frac{1}{2}I\sqrt{3} +\frac{\left(-4x(6x^2\log(x)-3x^2-4~\_C1)^2\right)^{(1/3)}} +{6x^2\log(x)-3*x^2-4~\_C1}$$ +$$-\frac{1}{2}\frac{\left(-4x(6x^2\log(x)-3x^2-4~\_C1)^2\right)^{(1/3)}} +{6x^2\log(x)-3*x^2-4~\_C1} +-\frac{1}{2}I\sqrt{3} +\frac{\left(-4x(6x^2\log(x)-3x^2-4~\_C1)^2\right)^{(1/3)}} +{6x^2\log(x)-3*x^2-4~\_C1}$$ +which, on substitution, simplifies to 0. + + +Mathematica gives 3 solutions, +$$\frac{(-2)^{2/3}x^{1/3}}{(3x^2+4C-6x^2\log(x))^{1/3}}$$ +$$\frac{( 2)^{2/3}x^{1/3}}{(3x^2+4C-6x^2\log(x))^{1/3}}$$ +$$\frac{(-1)^{1/3}2^{2/3}x^{1/3}}{(3x^2+4C-6x^2\log(x))^{1/3}}$$ +which do not simplify to 0 on substitution. +<<*>>= +--S 72 of 126 +yx:=solve(ode132,y,x) +--R +--R 2 3 2 3 +--R - 6x y(x) log(x) + 3x y(x) - 4x +--R (72) -------------------------------- +--R 3 +--R 4y(x) +--R Type: Union(Expression Integer,...) +--E 72 + +--S 73 of 126 +ode132expr := 3*x*D(yx,x) - 3*x*log(x)*yx**4 - yx +--R +--R (73) +--R 2 8 , 9 12 5 +--R 2304x y(x) y (x) - 3888x y(x) log(x) +--R +--R + +--R 9 12 8 9 4 +--R (7776x y(x) - 10368x y(x) )log(x) +--R + +--R 9 12 8 9 7 6 3 +--R (- 5832x y(x) + 15552x y(x) - 10368x y(x) )log(x) +--R + +--R 9 12 8 9 7 6 6 3 2 +--R (1944x y(x) - 7776x y(x) + 10368x y(x) - 4608x y(x) )log(x) +--R + +--R 9 2 12 8 9 7 6 6 3 +--R (- 243x - 1920x )y(x) + 1296x y(x) - 2592x y(x) + 2304x y(x) +--R + +--R 5 +--R - 768x +--R * +--R log(x) +--R + +--R 2 12 9 +--R - 192x y(x) - 512x y(x) +--R / +--R 12 +--R 256y(x) +--R Type: Expression Integer +--E 73 + +------------------------------------------------------------------- +--S 74 of 126 +ode133 := x**2*D(y(x),x) + y(x) - x +--R +--R 2 , +--R (74) x y (x) + y(x) - x +--R +--R Type: Expression Integer +--E 74 +@ +Maxima gets +$$\%e^{1/x} +\left(\int{\displaystyle\frac{\%e^{-\frac{1}{x}}}{x}}~dx+\%c\right)$$ +which, on substitution, simplifies to 0. + +Maple gives +$$\left({\rm Ei}\left(1,\frac{1}{x}\right)+~\_C1\right)e^{(\frac{1}{x})}$$ +which simplifies to 0 on substitution. + +Mathematica gets: +$$e^{1/x}C-e^{1/x}{\rm ExpIntegralEi}\left(-\frac{1}{x}\right)$$ +which simplifies to 0 on substitution. +<<*>>= +--S 75 of 126 +yx:=solve(ode133,y,x) +--R +--R +--R 1 1 +--R - x - +--R x ++ 1 x +--I (75) [particular= %e | ------- d%U ,basis= [%e ]] +--R ++ 1 +--R -- +--I %U +--I %U %e +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 75 + +------------------------------------------------------------------- +--S 76 of 126 +ode134 := x**2*D(y(x),x) - y(x) + x**2*exp(x-1/x) +--R +--R 2 +--R x - 1 +--R ------ +--R 2 , 2 x +--R (76) x y (x) + x %e - y(x) +--R +--R Type: Expression Integer +--E 76 +@ +Maxima gets +$$\%e^-\frac{1}{x}}\left(\%c-\%e^x\right$$ +which simplifies to 0 on substitution. + +Maple gets +$$(-e^x+~\_C1)e^{\left(-\frac{1}{x}\right)}$$ +which simplifies to 0 on substitution. + +Mathematics get +$$-e^{-\frac{1}{x}+x}+e^{-1/x}C$$ +which does not simplify to 0 on substitution. +This is curious because the basis element is the same one +computed by Axiom, which Axiom cannot simplify either. +However, Axiom can simplify the particular element to 0 +and Mathematica cannot. +<<*>>= +--S 77 of 126 +ode134a:=solve(ode134,y,x) +--R +--R 2 +--R x - 1 1 +--R ------ - - +--R x x +--R (77) [particular= - %e ,basis= [%e ]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 77 + +--S 78 of 126 +yx:=ode134a.particular +--R +--R 2 +--R x - 1 +--R ------ +--R x +--R (78) - %e +--R Type: Expression Integer +--E 78 + +--S 79 of 126 +ode134expr := x**2*D(yx,x) - yx + x**2*exp(x-1/x) +--R +--R (79) 0 +--R Type: Expression Integer +--E 79 + +------------------------------------------------------------------- +--S 80 of 126 +ode135 := x**2*D(y(x),x) - (x-1)*y(x) +--R +--R 2 , +--R (80) x y (x) + (- x + 1)y(x) +--R +--R Type: Expression Integer +--E 80 +@ +Maxima gets +$$\%c~x\%e^{1/x}$$ +which simplifies to 0 when substituted. + +Maple gets +$$\_C1xe^{\left(\frac{1}{x}\right)}$$ +which simplifies to 0 when substituted. + +Mathematica gets +$$e^{1/x}xC$$ +which simplifies to 0 when substituted. +<<*>>= +--S 81 of 126 +ode135a:=solve(ode135,y,x) +--R +--R 1 +--R - +--R x +--R (81) [particular= 0,basis= [x %e ]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 81 + +--S 82 of 126 +yx:=ode135a.particular +--R +--R (82) 0 +--R Type: Expression Integer +--E 82 + +--S 83 of 126 +ode135expr := x**2*D(yx,x) - (x-1)*yx +--R +--R (83) 0 +--R Type: Expression Integer +--E 83 + +------------------------------------------------------------------- +--S 84 of 126 +ode136 := x**2*D(y(x),x) + y(x)**2 + x*y(x) + x**2 +--R +--R 2 , 2 2 +--R (84) x y (x) + y(x) + x y(x) + x +--R +--R Type: Expression Integer +--E 84 +@ +Maxima gets +$$-\frac{x\log(\%c~x)-x}{log(\%c~x)}$$ +which simplifies to 0 on substitution. + +Maple gets +$$-\frac{x(-1+\log(x)+~\_C1)}{\log(x)+~\_C1}$$ +which simplifies to 0 on substitution. + +Mathematica gets +$$\frac{-x-xC+x\log(x)}{C-\log(x)}$$ +which simplifies to 0 on substition. +<<*>>= +--S 85 of 126 +yx:=solve(ode136,y,x) +--R +--R (- y(x) - x)log(x) + x +--R (85) ---------------------- +--R y(x) + x +--R Type: Union(Expression Integer,...) +--E 85 + +--S 86 of 126 +ode136expr := x**2*D(yx,x) + yx**2 + x*yx + x**2 +--R +--R (86) +--R 3 , 2 2 2 +--R - x y (x) + (y(x) + 2x y(x) + x )log(x) +--R +--R + +--R 2 2 3 2 2 2 3 +--R (- x y(x) + (- 2x - 2x)y(x) - x - 2x )log(x) + (x - x)y(x) + 2x y(x) +--R + +--R 4 2 +--R x + x +--R / +--R 2 2 +--R y(x) + 2x y(x) + x +--R Type: Expression Integer +--E 86 + +------------------------------------------------------------------- +--S 87 of 126 +ode137 := x**2*D(y(x),x) - y(x)**2 - x*y(x) +--R +--R 2 , 2 +--R (87) x y (x) - y(x) - x y(x) +--R +--R Type: Expression Integer +--E 87 +@ +Maxima gets +$$\frac{x}{\log\left(\displaystyle \frac{1}{\%c~x}\right)}$$ +which simplifies to 0 on substitution. + +Maple gets: +$$\frac{x}{-\log(x)+~\_C1}$$ +which simplifies to 0 on substitution. + +Mathematica gets: +$$\frac{x}{C-\log(x)}$$ +which simplifies to 0 on substitution. +<<*>>= +--S 88 of 126 +yx:=solve(ode137,y,x) +--R +--R y(x)log(x) + x +--R (88) -------------- +--R y(x) +--R Type: Union(Expression Integer,...) +--E 88 + +--S 89 of 126 +ode137expr := x**2*D(yx,x) - yx**2 - x*yx +--R +--R 3 , 2 2 2 2 2 +--R - x y (x) - y(x) log(x) + (- x y(x) - 2x y(x))log(x) + x y(x) - x +--R +--R (89) --------------------------------------------------------------------- +--R 2 +--R y(x) +--R Type: Expression Integer +--E 89 + +------------------------------------------------------------------- +--S 90 of 126 +ode138 := x**2*D(y(x),x) - y(x)**2 - x*y(x) - x**2 +--R +--R 2 , 2 2 +--R (90) x y (x) - y(x) - x y(x) - x +--R +--R Type: Expression Integer +--E 90 +@ +Maxima gets +$$\%c~x=\%e^{\arctan\left(\frac{y}{x}\right)}$$ +which does not simplify to 0 when substituted. + +Maple gets +$$\tan(\log(x)+~\_C1)x$$ +which simplifies to 0 on substitution. + +Mathematica get: +$$x\tan(C+\log(x))$$ +which simplifies to 0 when substituted. +<<*>>= + +--S 91 of 126 +yx:=solve(ode138,y,x) +--R +--R +---+ +---+ +--R (- 7\|- 1 + 9)y(x) + 9x\|- 1 + 7x +--R (91) -------------------------------------------------------- +--R +---+ +--R +---+ +---+ - 2\|- 1 log(x) +--R ((18\|- 1 + 14)y(x) - 14x\|- 1 + 18x)%e +--R Type: Union(Expression Integer,...) +--E 91 + +--S 92 of 126 +ode138expr := x**2*D(yx,x) - yx**2 - x*yx - x**2 +--R +--R (92) +--R 3 +---+ 3 4 +---+ 4 +--R ((- 1188x \|- 1 + 2716x )y(x) - 2716x \|- 1 - 1188x ) +--R * +--R +---+ +--R - 2\|- 1 log(x) , +--R %e y (x) +--R +--R + +--R 2 +---+ 2 3 3 +---+ 3 2 +--R (- 1188x \|- 1 + 2716x )y(x) + (- 8148x \|- 1 - 3564x )y(x) +--R + +--R 4 +---+ 4 5 +---+ 5 +--R (3564x \|- 1 - 8148x )y(x) + 2716x \|- 1 + 1188x +--R * +--R +---+ 2 +--R - 2\|- 1 log(x) +--R (%e ) +--R + +--R +---+ 3 2 +---+ 2 2 +--R (- 170x\|- 1 - 3310x)y(x) + (4498x \|- 1 - 2886x )y(x) +--R + +--R 3 +---+ 3 4 +---+ 4 +--R (2546x \|- 1 - 2122x )y(x) + 3310x \|- 1 - 170x +--R * +--R +---+ +--R - 2\|- 1 log(x) +--R %e +--R + +--R +---+ 3 +---+ 2 +--R (297\|- 1 - 679)y(x) + (- 679x\|- 1 - 297x)y(x) +--R + +--R 2 +---+ 2 3 +---+ 3 +--R (297x \|- 1 - 679x )y(x) - 679x \|- 1 - 297x +--R / +--R +---+ 3 +---+ 2 +--R (1188\|- 1 - 2716)y(x) + (8148x\|- 1 + 3564x)y(x) +--R + +--R 2 +---+ 2 3 +---+ 3 +--R (- 3564x \|- 1 + 8148x )y(x) - 2716x \|- 1 - 1188x +--R * +--R +---+ 2 +--R - 2\|- 1 log(x) +--R (%e ) +--R Type: Expression Integer +--E 92 + +------------------------------------------------------------------- +--S 93 of 126 +ode139 := x**2*(D(y(x),x)+y(x)**2) + a*x**k - b*(b-1) +--R +--R 2 , k 2 2 2 +--R (93) x y (x) + a x + x y(x) - b + b +--R +--R Type: Expression Integer +--E 93 + +@ +Maxima gets 6 answers, one of which is: +$$\frac{-\left(3^{5/6}\%i\left(ax^k+\%ckx-\%cx+b^2k-bk-b^2+b\right)^{1/3}- +3^{1/3}\left(ax^k+\%ckx-\%cx+b^2k-bk-b^2+b\right)^{1/3}\right)} +{\left(2(k-1)^{1/3}x^{1/3}\right)}$$ +which simplifies to 0 on substitution. +<<*>>= + +--S 94 of 126 +yx:=solve(ode139,y,x) +--R +--R (94) "failed" +--R Type: Union("failed",...) +--E 94 + +------------------------------------------------------------------- +--S 95 of 126 +ode140 := x**2*(D(y(x),x)+y(x)**2) + 4*x*y(x) + 2 +--R +--R 2 , 2 2 +--R (95) x y (x) + x y(x) + 4x y(x) + 2 +--R +--R Type: Expression Integer +--E 95 +@ +Maxima gets +$$-\frac{x-2\%c}{x^2-\%c~x}$$ +which simplifies to 0 when substituted. + +Maple gets +$$-\frac{-2~\_C1+x}{x(-~\_C1+x)}$$ +which simplifies to 0 when substituted. + +Mathematica gets: +$$-\frac{2}{x}+\frac{1}{x+C}$$ +which does not simplify. +<<*>>= +--S 96 of 126 +yx:=solve(ode140,y,x) +--R +--R x y(x) + 2 +--R (96) -------------------- +--R 2 +--R (x - x)y(x) + x - 2 +--R Type: Union(Expression Integer,...) +--E 96 + +--S 97 of 126 +ode140expr := x**2*(D(yx,x)+yx**2) + 4*x*yx + 2 +--R +--R (97) +--R 4 , 4 3 2 2 3 2 2 +--R - x y (x) + (6x - 8x + 2x )y(x) + (16x - 28x + 8x)y(x) + 12x - 24x + 8 +--R +--R ---------------------------------------------------------------------------- +--R 4 3 2 2 3 2 2 +--R (x - 2x + x )y(x) + (2x - 6x + 4x)y(x) + x - 4x + 4 +--R Type: Expression Integer +--E 97 + +------------------------------------------------------------------- +--S 98 of 126 +ode141 := x**2*(D(y(x),x)+y(x)**2) + a*x*y(x) + b +--R +--R 2 , 2 2 +--R (98) x y (x) + x y(x) + a x y(x) + b +--R +--R Type: Expression Integer +--E 98 + +@ +Maxima gets: +$$\%e^-a\log(x)-2x} +\left(\%c-b \int+\frac{\%e^a\log(x)+2x}}{x^2}}~dx\right$$ +which, when substituted, simplifies to 0. +<<*>>= + +--S 99 of 126 +yx:=solve(ode141,y,x) +--R 2 +--R WARNING (genufact): No known algorithm to factor ? + (a - 1)? + b +--R , trying square-free. +--R +--R (99) +--R +------------------+ +--R | 2 +--R \|- 4b + a - 2a + 1 - 2x y(x) - a + 1 +--R / +--R +------------------+ +--R | 2 2 +--R ((2x y(x) + a - 1)\|- 4b + a - 2a + 1 - 4b + a - 2a + 1) +--R * +--R +------------------+ +--R | 2 +--R - log(x)\|- 4b + a - 2a + 1 +--R %e +--R Type: Union(Expression Integer,...) +--E 99 + +--S 100 of 126 +ode141expr := x**2*(D(yx,x)+yx**2) + a*x*yx + b +--R +--R (100) +--R 2 4 3 2 3 +--R ((- 8b + 2a - 4a + 2)x y(x) + ((- 4a + 4)b + a - 3a + 3a - 1)x ) +--R * +--R +------------------+ +--R | 2 +--R \|- 4b + a - 2a + 1 +--R + +--R 2 2 4 3 2 3 +--R (16b + (- 8a + 16a - 8)b + a - 4a + 6a - 4a + 1)x +--R * +--R +------------------+ +--R | 2 +--R - log(x)\|- 4b + a - 2a + 1 , +--R %e y (x) +--R +--R + +--R 2 2 3 3 +--R (8b + (- 2a + 4a - 2)b)x y(x) +--R + +--R 2 3 2 2 2 +--R ((12a - 12)b + (- 3a + 9a - 9a + 3)b)x y(x) +--R + +--R 3 2 2 +--R - 24b + (18a - 36a + 18)b +--R + +--R 4 3 2 +--R (- 3a + 12a - 18a + 12a - 3)b +--R * +--R x y(x) +--R + +--R 3 3 2 2 +--R (- 12a + 12)b + (7a - 21a + 21a - 7)b +--R + +--R 5 4 3 2 +--R (- a + 5a - 10a + 10a - 5a + 1)b +--R * +--R +------------------+ +--R | 2 +--R \|- 4b + a - 2a + 1 +--R + +--R 3 2 2 4 3 2 2 +--R (- 48b + (24a - 48a + 24)b + (- 3a + 12a - 18a + 12a - 3)b)x +--R * +--R 2 +--R y(x) +--R + +--R 3 3 2 2 +--R (- 48a + 48)b + (24a - 72a + 72a - 24)b +--R + +--R 5 4 3 2 +--R (- 3a + 15a - 30a + 30a - 15a + 3)b +--R * +--R x y(x) +--R + +--R 4 2 3 4 3 2 2 +--R 16b + (- 24a + 48a - 24)b + (9a - 36a + 54a - 36a + 9)b +--R + +--R 6 5 4 3 2 +--R (- a + 6a - 15a + 20a - 15a + 6a - 1)b +--R * +--R +------------------+ 2 +--R | 2 +--R - log(x)\|- 4b + a - 2a + 1 +--R (%e ) +--R + +--R 2 4 3 +--R (- 8b + 2a - 4a + 2)x y(x) +--R + +--R 3 2 3 2 +--R ((- 16a + 4)b + 4a - 9a + 6a - 1)x y(x) +--R + +--R 2 2 4 3 2 2 +--R (- 8b + (- 6a + 4a + 2)b + 2a - 6a + 6a - 2a)x y(x) +--R + +--R 2 3 2 +--R ((- 8a + 4)b + (2a - 5a + 4a - 1)b)x +--R * +--R +------------------+ +--R | 2 +--R \|- 4b + a - 2a + 1 +--R + +--R 3 2 4 3 +--R (- 8a b + 2a - 4a + 2a)x y(x) +--R + +--R 2 2 4 3 2 3 2 +--R (16b + (- 20a + 28a - 8)b + 4a - 13a + 15a - 7a + 1)x y(x) +--R + +--R 2 3 2 5 4 3 2 2 +--R (8a b + (- 10a + 20a - 10a)b + 2a - 8a + 12a - 8a + 2a)x y(x) +--R + +--R 3 2 2 4 3 2 +--R (16b + (- 12a + 20a - 8)b + (2a - 7a + 9a - 5a + 1)b)x +--R * +--R +------------------+ +--R | 2 +--R - log(x)\|- 4b + a - 2a + 1 +--R %e +--R + +--R 5 3 4 2 2 3 +--R - 2x y(x) + (- 3a + 3)x y(x) + (- 2b - a + 2a - 1)x y(x) +--R + +--R 2 +--R (- a + 1)b x +--R * +--R +------------------+ +--R | 2 +--R \|- 4b + a - 2a + 1 +--R + +--R 2 4 2 3 2 3 +--R (- 4b + a - 2a + 1)x y(x) + ((- 4a + 4)b + a - 3a + 3a - 1)x y(x) +--R + +--R 2 2 2 +--R (- 4b + (a - 2a + 1)b)x +--R / +--R 2 3 3 +--R (8b - 2a + 4a - 2)x y(x) +--R + +--R 3 2 2 2 +--R ((12a - 12)b - 3a + 9a - 9a + 3)x y(x) +--R + +--R 2 2 4 3 2 +--R (- 24b + (18a - 36a + 18)b - 3a + 12a - 18a + 12a - 3)x y(x) +--R + +--R 2 3 2 5 4 3 2 +--R (- 12a + 12)b + (7a - 21a + 21a - 7)b - a + 5a - 10a + 10a +--R + +--R - 5a + 1 +--R * +--R +------------------+ +--R | 2 +--R \|- 4b + a - 2a + 1 +--R + +--R 2 2 4 3 2 2 2 +--R (- 48b + (24a - 48a + 24)b - 3a + 12a - 18a + 12a - 3)x y(x) +--R + +--R 2 3 2 5 4 3 +--R (- 48a + 48)b + (24a - 72a + 72a - 24)b - 3a + 15a - 30a +--R + +--R 2 +--R 30a - 15a + 3 +--R * +--R x y(x) +--R + +--R 3 2 2 4 3 2 6 +--R 16b + (- 24a + 48a - 24)b + (9a - 36a + 54a - 36a + 9)b - a +--R + +--R 5 4 3 2 +--R 6a - 15a + 20a - 15a + 6a - 1 +--R * +--R +------------------+ 2 +--R | 2 +--R - log(x)\|- 4b + a - 2a + 1 +--R (%e ) +--R Type: Expression Integer +--E 100 + +------------------------------------------------------------------- +--S 101 of 126 +ode142 := x**2*(D(y(x),x)-y(x)**2) - a*x**2*y(x) + a*x + 2 +--R +--R 2 , 2 2 2 +--R (101) x y (x) - x y(x) - a x y(x) + a x + 2 +--R +--R Type: Expression Integer +--E 101 + +@ +Maxima failed. +<<*>>= + +--S 102 of 126 +yx:=solve(ode142,y,x) +--R +--R 2 3 2 3 3 2 2 +--R (a x - 2a x + 2x)y(x) + a x - a x + 2a x - 2 +--R (102) ------------------------------------------------ +--R 3 3 - a x +--R (a x y(x) - a )%e +--R Type: Union(Expression Integer,...) +--E 102 + +--S 103 of 126 +ode142expr := x**2*(D(yx,x)-yx**2) - a*x**2*yx + a*x + 2 +--R +--R (103) +--R 6 6 - a x , +--R - a x %e y (x) +--R +--R + +--R 7 3 6 2 2 7 2 6 7 6 - a x 2 +--R ((a x + 2a x )y(x) + (- 2a x - 4a x)y(x) + a x + 2a )(%e ) +--R + +--R 5 5 4 4 2 6 5 5 4 4 3 6 4 5 3 +--R (2a x - 2a x )y(x) + (2a x - 4a x + 4a x )y(x) - 3a x + 2a x +--R + +--R 4 2 +--R - 2a x +--R * +--R - a x +--R %e +--R + +--R 4 8 3 7 2 6 5 4 2 +--R (- a x + 4a x - 8a x + 8a x - 4x )y(x) +--R + +--R 5 8 4 7 3 6 2 5 4 3 6 8 5 7 +--R (- 2a x + 6a x - 12a x + 16a x - 16a x + 8x )y(x) - a x + 2a x +--R + +--R 4 6 3 5 2 4 3 2 +--R - 5a x + 8a x - 8a x + 8a x - 4x +--R / +--R 6 2 2 6 6 - a x 2 +--R (a x y(x) - 2a x y(x) + a )(%e ) +--R Type: Expression Integer +--E 103 + +------------------------------------------------------------------- +--S 104 of 126 +ode143 := x**2*(D(y(x),x)+a*y(x)**2) - b +--R +--R 2 , 2 2 +--R (104) x y (x) + a x y(x) - b +--R +--R Type: Expression Integer +--E 104 + +@ +Maxima, if $4ab+1 >= 0$ gets: +$$x=\%c\%e^{ +-\frac{\displaystyle\log\left( +-\frac-2axy+\sqrt{4ab+1}+1} +2axy+\sqrt{4ab+1}-1}\right)} +{\displaystyle\sqrt{4ab+1}}$$ + +and if $4ab+1 < 0$ gets: +$$x=\%c\%e^{ +-\frac2\arctan\left( +\frac2axy-1}{\displaystyle\sqrt{-4ab-1}}\right)} +{\displaystyle\sqrt{-4ab-1}}$$ + +neither of which simplify to 0 on substitution. +<<*>>= + +--S 105 of 126 +yx:=solve(ode143,y,x) +--R 2 +--R WARNING (genufact): No known algorithm to factor ? - ? - a b +--R , trying square-free. +--R +--R +--------+ 2 +--R a\|4a b + 1 - 2a x y(x) + a +--R (105) ------------------------------------------------------------ +--R +--------+ +--R +--------+ - log(x)\|4a b + 1 +--R ((2a x y(x) - 1)\|4a b + 1 + 4a b + 1)%e +--R Type: Union(Expression Integer,...) +--E 105 + +--S 106 of 126 +ode143expr := x**2*(D(yx,x)+a*yx**2) - b +--R +--R (106) +--R +--------+ +--R 3 2 3 - log(x)\|4a b + 1 , +--R (- 8a b - 2a )x %e y (x) +--R +--R + +--R 2 2 2 +--------+ +--R ((- 8a b - 2a b)x y(x) + 4a b + b)\|4a b + 1 +--R + +--R 3 2 2 2 2 2 2 2 3 2 +--R (- 8a b - 2a b)x y(x) + (8a b + 2a b)x y(x) - 8a b - 6a b - b +--R * +--R +--------+ 2 +--R - log(x)\|4a b + 1 +--R (%e ) +--R + +--R +--------+ +--R 4 3 3 2 3 2 2 - log(x)\|4a b + 1 +--R ((- 8a b - 2a )x y(x) + (8a b + 2a b)x)%e +--R + +--R 4 3 3 2 +--------+ 5 4 2 4 3 4 3 2 +--R (- 2a x y(x) + a x )\|4a b + 1 + 2a x y(x) - 2a x y(x) + (2a b + a )x +--R / +--R 2 +--------+ 3 2 2 2 +--R ((8a b + 2a)x y(x) - 4a b - 1)\|4a b + 1 + (8a b + 2a )x y(x) +--R + +--R 2 2 2 +--R (- 8a b - 2a)x y(x) + 8a b + 6a b + 1 +--R * +--R +--------+ 2 +--R - log(x)\|4a b + 1 +--R (%e ) +--R Type: Expression Integer +--E 106 + +------------------------------------------------------------------- +--S 107 of 126 +ode144 := x**2*(D(y(x),x)+a*y(x)**2) + b*x**alpha + c +--R +--R 2 , alpha 2 2 +--R (107) x y (x) + b x + a x y(x) + c +--R +--R Type: Expression Integer +--E 107 + +@ +Maxima failed. +<<*>>= +--S 108 of 126 +yx:=solve(ode144,y,x) +--R +--R (108) "failed" +--R Type: Union("failed",...) +--E 108 + +------------------------------------------------------------------- +--S 109 of 126 +ode145 := x**2*D(y(x),x) + a*y(x)**3 - a*x**2*y(x)**2 +--R +--R 2 , 3 2 2 +--R (109) x y (x) + a y(x) - a x y(x) +--R +--R Type: Expression Integer +--E 109 + +@ +Maxima failed. + +Maple claims the result is 0, which when substituted, simplifies to 0 +<<*>>= +--S 110 of 126 +yx:=solve(ode145,y,x) +--R +--R (110) "failed" +--R Type: Union("failed",...) +--E 110 + +------------------------------------------------------------------- +--S 111 of 126 +ode146 := x**2*D(y(x),x) + x*y(x)**3 + a*y(x)**2 +--R +--R 2 , 3 2 +--R (111) x y (x) + x y(x) + a y(x) +--R +--R Type: Expression Integer +--E 111 + +@ +Maxima failed. + +Maple gets 0 which, when substituted, simplifies to 0. +<<*>>= +--S 112 of 126 +yx:=solve(ode146,y,x) +--R +--R (112) "failed" +--R Type: Union("failed",...) +--E 112 + +------------------------------------------------------------------- +--S 113 of 126 +ode147 := x**2*D(y(x),x) + a*x**2*y(x)**3 + b*y(x)**2 +--R +--R 2 , 2 3 2 +--R (113) x y (x) + a x y(x) + b y(x) +--R +--R Type: Expression Integer +--E 113 +@ +Maxima failed. + +Maple gets 0 which, when substituted, results in 0. +<<*>>= +--S 114 of 126 +yx:=solve(ode147,y,x) +--R +--R (114) "failed" +--R Type: Union("failed",...) +--E 114 + +------------------------------------------------------------------- +--S 115 of 126 +ode148 := (x**2+1)*D(y(x),x) + x*y(x) - 1 +--R +--R 2 , +--R (115) (x + 1)y (x) + x y(x) - 1 +--R +--R Type: Expression Integer +--E 115 +@ +Maxima gets +$$({\rm asinh}(x)+\%c)\%e^{-\frac{\displaystyle\log(x^2+1)}2}$$ +which when substituted, does not simplify to 0. + +Maple gets +$$\frac{{\rm arcsinh}(x)+~\_C1}{\sqrt{x^2+1}}$$ +which when substituted, simplifies to 0. + +Mathematica gets +$$\frac{{\rm arcsinh}(x)}{\sqrt{1+x^2}}+\frac{C}{\sqrt{1+x^2}}$$ +gives 0 when substituted. +<<*>>= +--S 116 of 126 +ode148a:=solve(ode148,y,x) +--R +--R +------+ +--R | 2 +--R log(\|x + 1 - x) 1 +--R (116) [particular= - ------------------,basis= [---------]] +--R +------+ +------+ +--R | 2 | 2 +--R \|x + 1 \|x + 1 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 116 + +--S 117 of 126 +yx:=ode148a.particular +--R +--R +------+ +--R | 2 +--R log(\|x + 1 - x) +--R (117) - ------------------ +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression Integer +--E 117 + +--S 118 of 126 +ode148expr := (x**2+1)*D(yx,x) + x*yx - 1 +--R +--R (118) 0 +--R Type: Expression Integer +--E 118 + +------------------------------------------------------------------- +--S 119 of 126 +ode149 := (x**2+1)*D(y(x),x) + x*y(x) - x*(x**2+1) +--R +--R 2 , 3 +--R (119) (x + 1)y (x) + x y(x) - x - x +--R +--R Type: Expression Integer +--E 119 +@ +Maxima gets +$$\left(\displaystyle\frac{(x^2+1)^{3/2}}{3}+\%c\right) +\%e^-\frac{log(x^2+1)}{2}$$ +which simplifies to 0 when substituted. + +Maple gets +$$\frac{x^2}{3}+\frac{1}{3}+\frac{\_C1}{\sqrt{x^2+1}}$$ +which simplifies to 0 when substituted. + +Mathematica gets +$$\frac{1}{3}(1+x^2)+\frac{C}{\sqrt{1+x^2}}$$ +which simplifes to 0 when substituted. +<<*>>= +--S 120 of 126 +ode149a:=solve(ode149,y,x) +--R +--R 2 +--R x + 1 1 +--R (120) [particular= ------,basis= [---------]] +--R 3 +------+ +--R | 2 +--R \|x + 1 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 120 + +--S 121 of 126 +yx:=ode149a.particular +--R +--R 2 +--R x + 1 +--R (121) ------ +--R 3 +--R Type: Expression Integer +--E 121 + +--S 122 of 126 +ode149expr := (x**2+1)*D(yx,x) + x*yx - x*(x**2+1) +--R +--R (122) 0 +--R Type: Expression Integer +--E 122 + +------------------------------------------------------------------- +--S 123 of 126 +ode150 := (x**2+1)*D(y(x),x) + 2*x*y(x) - 2*x**2 +--R +--R 2 , 2 +--R (123) (x + 1)y (x) + 2x y(x) - 2x +--R +--R Type: Expression Integer +--E 123 +@ +Maxima gets +$$\displaystyle\frac{\frac{2x^3}{3}+\%c}{x^2+1}$$ +which simplifies to 0 on substitution. + +Maple gets +$$\frac{\frac{2x^3}{3}+~\_C1}{x^2+1}$$ +which simplifies to 0 on substitution. + +Mathematica gets: +$$\frac{2x^3}{3(1+x^2)}+\frac{C}{1+x^2}$$ +which simplifies to 0 on substitution. +<<*>>= + +--S 124 of 126 +ode150a:=solve(ode150,y,x) +--R +--R 3 +--R 2x + 3 1 +--R (124) [particular= -------,basis= [------]] +--R 2 2 +--R 3x + 3 x + 1 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 124 + +--S 125 of 126 +yx:=ode150a.particular +--R +--R 3 +--R 2x + 3 +--R (125) ------- +--R 2 +--R 3x + 3 +--R Type: Expression Integer +--E 125 + +--S 126 of 126 +ode150expr := (x**2+1)*D(yx,x) + 2*x*yx - 2*x**2 +--R +--R (126) 0 +--R Type: Expression Integer +--E 126 +)spool +)lisp (bye) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} {\bf http://www.cs.uwaterloo.ca/$\tilde{}$ecterrab/odetools.html} +\bibitem{2} Mathematica 6.0.1.0 +\bibitem{3} Maple 11.01 Build ID 296069 +\bibitem{4} Maxima 5.13.0 +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/kamke2.input.pdf b/src/axiom-website/CATS/kamke2.input.pdf new file mode 100644 index 0000000..040a890 Binary files /dev/null and b/src/axiom-website/CATS/kamke2.input.pdf differ diff --git a/src/axiom-website/CATS/kamke3.input.pamphlet b/src/axiom-website/CATS/kamke3.input.pamphlet new file mode 100644 index 0000000..fc280ab --- /dev/null +++ b/src/axiom-website/CATS/kamke3.input.pamphlet @@ -0,0 +1,2682 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input kamke3.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This is the first 50 of the Kamke test suite as published by +E. S. Cheb-Terrab\cite{1}. They have been rewritten using Axiom +syntax. Where possible we show that the particular solution actually +satisfies the original ordinary differential equation. +\end{abstract} +\eject +\tableofcontents +\eject +<<*>>= +)spool kamke3.output +)set break resume +)set mes auto off +)clear all + +--S 1 of 139 +y:=operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 1 + +--S 2 of 139 +ode151 := (x**2+1)*D(y(x),x) + (y(x)**2+1)*(2*x*y(x) - 1) +--R +--R +--R 2 , 3 2 +--R (2) (x + 1)y (x) + 2x y(x) - y(x) + 2x y(x) - 1 +--R +--R Type: Expression Integer +--E 2 + +--S 3 of 139 +ode151a:=solve(ode151,y,x) +--R +--R +--R (3) "failed" +--R Type: Union("failed",...) +--E 3 + +--S 4 of 139 +ode152 := (x**2+1)*D(y(x),x) + x*sin(y(x))*cos(y(x)) - x*(x**2+1)*cos(y(x))**2 +--R +--R +--R 2 , 3 2 +--R (4) (x + 1)y (x) + x cos(y(x))sin(y(x)) + (- x - x)cos(y(x)) +--R +--R Type: Expression Integer +--E 4 + +--S 5 of 139 +ode152a:=solve(ode152,y,x) +--R +--R +--R (5) "failed" +--R Type: Union("failed",...) +--E 5 + +--S 6 of 139 +ode153 := (x**2-1)*D(y(x),x) - x*y(x) + a +--R +--R +--R 2 , +--R (6) (x - 1)y (x) - x y(x) + a +--R +--R Type: Expression Integer +--E 6 + +--S 7 of 139 +ode153a:=solve(ode153,y,x) +--R +--R +--R +------+ +--R | 2 +--R (7) [particular= a x,basis= [\|x - 1 ]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 7 + +--S 8 of 139 +yx:=ode153a.particular +--R +--R +--R (8) a x +--R Type: Expression Integer +--E 8 + +--S 9 of 139 +ode153expr := (x**2-1)*D(yx,x) - x*yx + a +--R +--R +--R (9) 0 +--R Type: Expression Integer +--E 9 + +--S 10 of 139 +ode154 := (x**2-1)*D(y(x),x) + 2*x*y(x) - cos(x) +--R +--R +--R 2 , +--R (10) (x - 1)y (x) - cos(x) + 2x y(x) +--R +--R Type: Expression Integer +--E 10 + +--S 11 of 139 +ode154a:=solve(ode154,y,x) +--R +--R +--R sin(x) 1 +--R (11) [particular= ------,basis= [------]] +--R 2 2 +--R x - 1 x - 1 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 11 + +--S 12 of 139 +yx:=ode154a.particular +--R +--R +--R sin(x) +--R (12) ------ +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 12 + +--S 13 of 139 +ode154expr := (x**2-1)*D(yx,x) + 2*x*yx - cos(x) +--R +--R +--R (13) 0 +--R Type: Expression Integer +--E 13 + +--S 14 of 139 +ode155 := (x**2-1)*D(y(x),x) + y(x)**2 - 2*x*y(x) + 1 +--R +--R +--R 2 , 2 +--R (14) (x - 1)y (x) + y(x) - 2x y(x) + 1 +--R +--R Type: Expression Integer +--E 14 + +--S 15 of 139 +yx:=solve(ode155,y,x) +--R +--R +--R (y(x) - x)log(x + 1) + (- y(x) + x)log(x - 1) + 2 +--R (15) ------------------------------------------------- +--R 2y(x) - 2x +--R Type: Union(Expression Integer,...) +--E 15 + +--S 16 of 139 +ode155expr := (x**2-1)*D(yx,x) + yx**2 - 2*x*yx + 1 +--R +--R +--R (16) +--R 2 , 2 2 2 +--R (- 4x + 4)y (x) + (y(x) - 2x y(x) + x )log(x + 1) +--R +--R + +--R 2 2 2 2 3 +--R (- 2y(x) + 4x y(x) - 2x )log(x - 1) - 4x y(x) + (8x + 4)y(x) - 4x +--R + +--R - 4x +--R * +--R log(x + 1) +--R + +--R 2 2 2 +--R (y(x) - 2x y(x) + x )log(x - 1) +--R + +--R 2 2 3 2 +--R (4x y(x) + (- 8x - 4)y(x) + 4x + 4x)log(x - 1) - 8x y(x) + 12x +--R / +--R 2 2 +--R 4y(x) - 8x y(x) + 4x +--R Type: Expression Integer +--E 16 + +--S 17 of 139 +ode156 := (x**2-1)*D(y(x),x) - y(x)*(y(x)-x) +--R +--R +--R 2 , 2 +--R (17) (x - 1)y (x) - y(x) + x y(x) +--R +--R Type: Expression Integer +--E 17 + +--S 18 of 139 +yx:=solve(ode156,y,x) +--R +--R +--R - x y(x) + 1 +--R (18) ------------- +--R +------+ +--R | 2 +--R y(x)\|x - 1 +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 139 +ode156expr := (x**2-1)*D(yx,x) - yx*(yx-x) +--R +--R +--R (19) +--R +------+ +--R 4 2 , 2 2 | 2 +--R (- x + 2x - 1)y (x) + (- x y(x) + 2x y(x) - 1)\|x - 1 +--R +--R + +--R 4 2 2 +--R (- x + 2x - 1)y(x) +--R / +--R +------+ +--R 2 2 | 2 +--R (x - 1)y(x) \|x - 1 +--R Type: Expression Integer +--E 19 + +--S 20 of 139 +ode157 := (x**2-1)*D(y(x),x) + a*(y(x)**2-2*x*y(x)+1) +--R +--R +--R 2 , 2 +--R (20) (x - 1)y (x) + a y(x) - 2a x y(x) + a +--R +--R Type: Expression Integer +--E 20 + +--S 21 of 139 +ode157a:=solve(ode157,y,x) +--R +--R +--R (21) "failed" +--R Type: Union("failed",...) +--E 21 + +--S 22 of 139 +ode158 := (x**2-1)*D(y(x),x) + a*x*y(x)**2 + x*y(x) +--R +--R +--R 2 , 2 +--R (22) (x - 1)y (x) + a x y(x) + x y(x) +--R +--R Type: Expression Integer +--E 22 + +--S 23 of 139 +yx:=solve(ode158,y,x) +--R +--R +--R 2 2 2 +--R a x y(x) + 2a y(x) + 1 +--R (23) ------------------------ +--R 4 2 3 2 +--R 2a y(x) + 4a y(x) + 2a +--R Type: Union(Expression Integer,...) +--E 23 + +--S 24 of 139 +ode158expr := (x**2-1)*D(yx,x) + a*x*yx**2 + x*yx +--R +--R +--R (24) +--R 4 4 4 2 4 2 3 4 3 2 3 , +--R ((4a x - 8a x + 4a )y(x) + (4a x - 8a x + 4a )y(x))y (x) +--R +--R + +--R 4 5 5 3 5 4 4 3 3 4 3 +--R (a x + 6a x - 4a x)y(x) + ((12a + 4a )x - 4a x)y(x) +--R + +--R 3 2 3 3 2 2 2 +--R ((6a + 2a )x + (6a + 4a )x)y(x) + (8a + 4a)x y(x) + (2a + 1)x +--R / +--R 7 4 6 3 5 2 4 3 +--R 4a y(x) + 16a y(x) + 24a y(x) + 16a y(x) + 4a +--R Type: Expression Integer +--E 24 + +--S 25 of 139 +ode159 := (x**2-1)*D(y(x),x) - 2*x*y(x)*log(y(x)) +--R +--R +--R 2 , +--R (25) (x - 1)y (x) - 2x y(x)log(y(x)) +--R +--R Type: Expression Integer +--E 25 + +--S 26 of 139 +yx:=solve(ode159,y,x) +--R +--R +--R 2 +--R - x + 1 +--R (26) --------- +--R log(y(x)) +--R Type: Union(Expression Integer,...) +--E 26 + +--S 27 of 139 +ode159expr := (x**2-1)*D(yx,x) - 2*x*yx*log(yx) +--R +--R +--R (27) +--R 2 +--R 3 - x + 1 4 2 , +--R (2x - 2x)y(x)log(y(x))log(---------) + (x - 2x + 1)y (x) +--R log(y(x)) +--R + +--R 3 +--R (- 2x + 2x)y(x)log(y(x)) +--R / +--R 2 +--R y(x)log(y(x)) +--R Type: Expression Integer +--E 27 + +--S 28 of 139 +ode160 := (x**2-4)*D(y(x),x) + (x+2)*y(x)**2 - 4*y(x) +--R +--R +--R 2 , 2 +--R (28) (x - 4)y (x) + (x + 2)y(x) - 4y(x) +--R +--R Type: Expression Integer +--E 28 + +--S 29 of 139 +yx:=solve(ode160,y,x) +--R +--R +--R (- x - 2)y(x)log(x + 2) + x - 2 +--R (29) ------------------------------- +--R (x + 2)y(x) +--R Type: Union(Expression Integer,...) +--E 29 + +--S 30 of 139 +ode160expr := (x**2-4)*D(yx,x) + (x+2)*yx**2 - 4*yx +--R +--R +--R (30) +--R 3 2 , 2 2 2 +--R (- x + 2x + 4x - 8)y (x) + (x + 4x + 4)y(x) log(x + 2) +--R +--R + +--R 2 2 2 2 2 +--R ((4x + 8)y(x) + (- 2x + 8)y(x))log(x + 2) + (- x + 4)y(x) + x - 4x + 4 +--R / +--R 2 +--R (x + 2)y(x) +--R Type: Expression Integer +--E 30 + +--S 31 of 139 +ode161 := (x**2-5*x+6)*D(y(x),x) + 3*x*y(x) - 8*y(x) + x**2 +--R +--R +--R 2 , 2 +--R (31) (x - 5x + 6)y (x) + (3x - 8)y(x) + x +--R +--R Type: Expression Integer +--E 31 + +--S 32 of 139 +ode161a:=solve(ode161,y,x) +--R +--R +--R 4 3 +--R - 3x + 8x - 144 1 +--R (32) [particular= ------------------------,basis= [-------------------]] +--R 3 2 3 2 +--R 12x - 84x + 192x - 144 x - 7x + 16x - 12 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 32 + +--S 33 of 139 +yx:=ode161a.particular +--R +--R +--R 4 3 +--R - 3x + 8x - 144 +--R (33) ------------------------ +--R 3 2 +--R 12x - 84x + 192x - 144 +--R Type: Expression Integer +--E 33 + +--S 34 of 139 +ode161expr := (x**2-5*x+6)*D(yx,x) + 3*x*yx - 8*yx + x**2 +--R +--R +--R (34) 0 +--R Type: Expression Integer +--E 34 + +--S 35 of 139 +ode162 := (x-a)*(x-b)*D(y(x),x) + y(x)**2 + k*(y(x)+x-a)*(y(x)+x-b) +--R +--R +--R (35) +--R 2 , 2 +--R (x + (- b - a)x + a b)y (x) + (k + 1)y(x) + (2k x + (- b - a)k)y(x) +--R +--R + +--R 2 +--R k x + (- b - a)k x + a b k +--R Type: Expression Integer +--E 35 +@ +This loops infinitely +\begin{verbatim} +ode162a:=solve(ode162,y,x) + + WARNING (genufact): No known algorithm to factor + 3 2 2 2 + ? - 3? + (- k + 3)? + k - 1, trying square-free. + +\end{verbatim} +<<*>>= +--S 36 of 139 +ode163 := 2*x**2*D(y(x),x) - 2*y(x)**2 - x*y(x) + 2*a**2*x +--R +--R +--R 2 , 2 2 +--R (36) 2x y (x) - 2y(x) - x y(x) + 2a x +--R +--R Type: Expression Integer +--E 36 + +--S 37 of 139 +yx:=solve(ode163,y,x) +--R +--R +--R +-+ +--R a\|x - y(x) +--R (37) --------------------------- +--R 4a +--R - ---- +--R +-+ +--R 2 +-+ \|x +--R (2a \|x + 2a y(x))%e +--R Type: Union(Expression Integer,...) +--E 37 + +--S 38 of 139 +ode163expr := 2*x**2*D(yx,x) - 2*yx**2 - x*yx + 2*a**2*x +--R +--R +--R (38) +--R 4a +--R - ---- +--R +-+ +--R 3 3 2 5 4 +-+ 2 3 3 4 4 \|x , +--R ((- 12a x y(x) - 4a x )\|x - 4a x y(x) - 12a x y(x))%e y (x) +--R +--R + +--R 4 5 6 2 3 8 3 +-+ 5 2 4 +--R (4a x y(x) + 40a x y(x) + 20a x y(x))\|x + 20a x y(x) +--R + +--R 7 3 2 9 4 +--R 40a x y(x) + 4a x +--R * +--R 4a 2 +--R - ---- +--R +-+ +--R \|x +--R (%e ) +--R + +--R 5 3 4 3 2 3 5 2 2 5 3 +--R a x y(x) + 12a x y(x) + 8a x y(x) - 8a x y(x) - a x y(x) +--R + +--R 7 3 +--R - 4a x +--R * +--R +-+ +--R \|x +--R + +--R 2 5 2 2 4 4 2 3 4 3 2 6 3 6 4 +--R 4a x y(x) + 5a x y(x) + 8a x y(x) + 4a x y(x) - 12a x y(x) - a x +--R * +--R 4a +--R - ---- +--R +-+ +--R \|x +--R %e +--R + +--R 5 2 3 4 2 +-+ 4 3 2 2 5 3 +--R (- y(x) + 2a x y(x) - a x y(x))\|x - a x y(x) + 2a x y(x) - a x +--R / +--R 2 5 4 3 6 2 +-+ 3 4 5 2 2 +--R (2a y(x) + 20a x y(x) + 10a x y(x))\|x + 10a x y(x) + 20a x y(x) +--R + +--R 7 3 +--R 2a x +--R * +--R 4a 2 +--R - ---- +--R +-+ +--R \|x +--R (%e ) +--R Type: Expression Integer +--E 38 + +--S 39 of 139 +ode164 := 2*x**2*D(y(x),x) - 2*y(x)**2 - 3*x*y(x) + 2*a**2*x +--R +--R +--R 2 , 2 2 +--R (39) 2x y (x) - 2y(x) - 3x y(x) + 2a x +--R +--R Type: Expression Integer +--E 39 + +--S 40 of 139 +yx:=solve(ode164,y,x) +--R +--R +--R +-+ +--R (- 2y(x) - x)\|x + 2a x +--R (40) ------------------------------------- +--R 4a +--R - ---- +--R +-+ +--R +-+ 2 \|x +--R ((4a y(x) + 2a x)\|x + 4a x)%e +--R Type: Union(Expression Integer,...) +--E 40 + +--S 41 of 139 +ode164expr := 2*x**2*D(yx,x) - 2*yx**2 - 3*x*yx + 2*a**2*x +--R +--R +--R (41) +--R 2 2 3 2 3 2 2 4 4 3 2 5 +--R - 128a x y(x) - 192a x y(x) + (- 96a x - 384a x )y(x) - 16a x +--R + +--R 4 4 +--R - 192a x +--R * +--R +-+ +--R \|x +--R + +--R 3 3 2 3 4 3 5 5 4 +--R - 384a x y(x) - 384a x y(x) - 96a x - 128a x +--R * +--R 4a +--R - ---- +--R +-+ +--R \|x , +--R %e y (x) +--R +--R + +--R 5 4 5 2 3 5 3 7 2 2 +--R 640a x y(x) + 1280a x y(x) + (960a x + 1280a x )y(x) +--R + +--R 5 4 7 3 5 5 7 4 9 3 +--R (320a x + 1280a x )y(x) + 40a x + 320a x + 128a x +--R * +--R +-+ +--R \|x +--R + +--R 4 5 4 2 4 4 3 6 2 3 +--R 128a x y(x) + 320a x y(x) + (320a x + 1280a x )y(x) +--R + +--R 4 4 6 3 2 4 5 6 4 8 3 4 6 +--R (160a x + 1920a x )y(x) + (40a x + 960a x + 640a x )y(x) + 4a x +--R + +--R 6 5 8 4 +--R 160a x + 320a x +--R * +--R 4a 2 +--R - ---- +--R +-+ +--R \|x +--R (%e ) +--R + +--R 2 5 2 4 2 2 4 3 +--R 128a y(x) + 672a x y(x) + (960a x + 256a x)y(x) +--R + +--R 2 3 4 2 2 2 4 6 2 2 5 +--R (592a x + 384a x )y(x) + (168a x - 384a x )y(x) + 18a x +--R + +--R 4 4 6 3 +--R - 64a x - 288a x +--R * +--R +-+ +--R \|x +--R + +--R 5 2 3 4 3 3 2 3 +--R 96a x y(x) + (240a x + 384a x)y(x) + (240a x + 1152a x )y(x) +--R + +--R 4 3 3 5 2 2 5 3 4 5 3 +--R (120a x + 960a x - 256a x )y(x) + (30a x + 288a x - 480a x )y(x) +--R + +--R 6 3 5 5 4 7 3 +--R 3a x + 24a x - 240a x - 128a x +--R * +--R 4a +--R - ---- +--R +-+ +--R \|x +--R %e +--R + +--R 4 3 2 3 2 +--R - 32a y(x) - 64a x y(x) + (- 48a x + 64a x)y(x) +--R + +--R 3 3 2 4 3 3 5 2 +--R (- 16a x + 64a x )y(x) - 2a x + 16a x - 32a x +--R * +--R +-+ +--R \|x +--R + +--R 5 4 2 2 3 3 2 2 2 +--R - 32y(x) - 80x y(x) + (- 80x + 64a x)y(x) + (- 40x + 96a x )y(x) +--R + +--R 4 2 3 4 2 5 2 4 4 3 +--R (- 10x + 48a x - 32a x )y(x) - x + 8a x - 16a x +--R / +--R 3 4 3 3 3 2 5 2 +--R 320a y(x) + 640a x y(x) + (480a x + 640a x)y(x) +--R + +--R 3 3 5 2 3 4 5 3 7 2 +--R (160a x + 640a x )y(x) + 20a x + 160a x + 64a x +--R * +--R +-+ +--R \|x +--R + +--R 2 5 2 4 2 2 4 3 +--R 64a y(x) + 160a x y(x) + (160a x + 640a x)y(x) +--R + +--R 2 3 4 2 2 2 4 4 3 6 2 2 5 +--R (80a x + 960a x )y(x) + (20a x + 480a x + 320a x )y(x) + 2a x +--R + +--R 4 4 6 3 +--R 80a x + 160a x +--R * +--R 4a 2 +--R - ---- +--R +-+ +--R \|x +--R (%e ) +--R Type: Expression Integer +--E 41 + +--S 42 of 139 +ode165 := x*(2*x-1)*D(y(x),x) + y(x)**2 - (4*x+1)*y(x) + 4*x +--R +--R +--R 2 , 2 +--R (42) (2x - x)y (x) + y(x) + (- 4x - 1)y(x) + 4x +--R +--R Type: Expression Integer +--E 42 + +--S 43 of 139 +yx:=solve(ode165,y,x) +--R +--R +--R 2 +--R x y(x) - 2x +--R (43) ------------ +--R y(x) - 1 +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 139 +ode165expr := x*(2*x-1)*D(yx,x) + yx**2 - (4*x+1)*yx + 4*x +--R +--R +--R (44) +--R 4 3 2 , 2 2 3 2 4 +--R (4x - 4x + x )y (x) + (- x + 2x)y(x) + (- 4x + 8x - 6x)y(x) + 4x +--R +--R + +--R 2 +--R - 6x + 4x +--R / +--R 2 +--R y(x) - 2y(x) + 1 +--R Type: Expression Integer +--E 44 + +--S 45 of 139 +ode166 := 2*x*(x-1)*D(y(x),x) + (x-1)*y(x)**2 - x +--R +--R +--R 2 , 2 +--R (45) (2x - 2x)y (x) + (x - 1)y(x) - x +--R +--R Type: Expression Integer +--E 45 + +--S 46 of 139 +ode166a:=solve(ode166,y,x) +--R +--R +--R (46) "failed" +--R Type: Union("failed",...) +--E 46 + +--S 47 of 139 +ode167 := 3*x**2*D(y(x),x) - 7*y(x)**2 - 3*x*y(x) - x**2 +--R +--R +--R 2 , 2 2 +--R (47) 3x y (x) - 7y(x) - 3x y(x) - x +--R +--R Type: Expression Integer +--E 47 + +--S 48 of 139 +yx:=solve(ode167,y,x) +--R +--R +--R +---+ +---+ +--R (- 497\|- 7 + 1197)y(x) + 171x\|- 7 + 497x +--R (48) ------------------------------------------------------------ +--R +---+ +--R 2\|- 7 log(x) +--R - ------------- +--R +---+ +---+ 3 +--R ((342\|- 7 + 994)y(x) - 142x\|- 7 + 342x)%e +--R Type: Union(Expression Integer,...) +--E 48 + +--S 49 of 139 +ode167expr := 3*x**2*D(yx,x) - 7*yx**2 - 3*x*yx - x**2 +--R +--R +--R (49) +--R 3 +---+ 3 4 +---+ +--R (- 275142420x \|- 7 + 547274532x )y(x) - 78182076x \|- 7 +--R + +--R 4 +--R - 275142420x +--R * +--R +---+ +--R 2\|- 7 log(x) +--R - ------------- +--R 3 , +--R %e y (x) +--R +--R + +--R 2 +---+ 2 3 +--R (- 91714140x \|- 7 + 182424844x )y(x) +--R + +--R 3 +---+ 3 2 +--R (- 78182076x \|- 7 - 275142420x )y(x) +--R + +--R 4 +---+ 4 5 +---+ 5 +--R (39306060x \|- 7 - 78182076x )y(x) + 3722956x \|- 7 + 13102020x +--R * +--R +---+ 2 +--R 2\|- 7 log(x) +--R - ------------- +--R 3 +--R (%e ) +--R + +--R +---+ 3 +--R (368361714x\|- 7 - 2239972378x)y(x) +--R + +--R 2 +---+ 2 2 +--R (595138474x \|- 7 - 178912818x )y(x) +--R + +--R 3 +---+ 3 4 +---+ 4 +--R (130805178x \|- 7 - 44853634x )y(x) + 45713722x \|- 7 + 52623102x +--R * +--R +---+ +--R 2\|- 7 log(x) +--R - ------------- +--R 3 +--R %e +--R + +--R +---+ 3 +--R (1123498215\|- 7 - 2234704339)y(x) +--R + +--R +---+ 2 +--R (- 319243477x\|- 7 - 1123498215x)y(x) +--R + +--R 2 +---+ 2 3 +---+ 3 +--R (160499745x \|- 7 - 319243477x )y(x) - 45606211x \|- 7 - 160499745x +--R / +--R +---+ 3 +---+ 2 +--R (91714140\|- 7 - 182424844)y(x) + (78182076x\|- 7 + 275142420x)y(x) +--R + +--R 2 +---+ 2 3 +---+ 3 +--R (- 39306060x \|- 7 + 78182076x )y(x) - 3722956x \|- 7 - 13102020x +--R * +--R +---+ 2 +--R 2\|- 7 log(x) +--R - ------------- +--R 3 +--R (%e ) +--R Type: Expression Integer +--E 49 + +--S 50 of 139 +ode168 := 3*(x**2-4)*D(y(x),x) + y(x)**2 - x*y(x) - 3 +--R +--R +--R 2 , 2 +--R (50) (3x - 12)y (x) + y(x) - x y(x) - 3 +--R +--R Type: Expression Integer +--E 50 + +--S 51 of 139 +ode168a:=solve(ode168,y,x) +--R +--R +--R (51) "failed" +--R Type: Union("failed",...) +--E 51 + +--S 52 of 139 +ode169 := (a*x+b)**2*D(y(x),x) + (a*x+b)*y(x)**3 + c*y(x)**2 +--R +--R +--R 2 2 2 , 3 2 +--R (52) (a x + 2a b x + b )y (x) + (a x + b)y(x) + c y(x) +--R +--R Type: Expression Integer +--E 52 + +--S 53 of 139 +ode169a:=solve(ode169,y,x) +--R +--R +--R (53) "failed" +--R Type: Union("failed",...) +--E 53 + +--S 54 of 139 +ode170 := x**3*D(y(x),x) - y(x)**2 - x**4 +--R +--R +--R 3 , 2 4 +--R (54) x y (x) - y(x) - x +--R +--R Type: Expression Integer +--E 54 + +--S 55 of 139 +yx:=solve(ode170,y,x) +--R +--R +--R 2 2 +--R (y(x) - x )log(x) + x +--R (55) ---------------------- +--R 2 +--R y(x) - x +--R Type: Union(Expression Integer,...) +--E 55 + +--S 56 of 139 +ode170expr := x**3*D(yx,x) - yx**2 - x**4 +--R +--R +--R (56) +--R 5 , 2 2 4 2 2 4 +--R - x y (x) + (- y(x) + 2x y(x) - x )log(x) + (- 2x y(x) + 2x )log(x) +--R +--R + +--R 4 2 2 6 8 6 4 +--R (- x + x )y(x) + 2x y(x) - x + x - x +--R / +--R 2 2 4 +--R y(x) - 2x y(x) + x +--R Type: Expression Integer +--E 56 + +--S 57 of 139 +ode171 := x**3*D(y(x),x) - y(x)**2 - x**2*y(x) +--R +--R +--R 3 , 2 2 +--R (57) x y (x) - y(x) - x y(x) +--R +--R Type: Expression Integer +--E 57 + +--S 58 of 139 +yx:=solve(ode171,y,x) +--R +--R +--R 2 +--R - y(x) + x +--R (58) ----------- +--R x y(x) +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 of 139 +ode171expr := x**3*D(yx,x) - yx**2 - x**2*yx +--R +--R +--R 6 , 3 2 2 4 +--R - x y (x) + (2x - 1)y(x) + 2x y(x) - x +--R +--R (59) ----------------------------------------- +--R 2 2 +--R x y(x) +--R Type: Expression Integer +--E 59 + +--S 60 of 139 +ode172 := x**3*D(y(x),x) - x**4*y(x)**2 + x**2*y(x) + 20 +--R +--R +--R 3 , 4 2 2 +--R (60) x y (x) - x y(x) + x y(x) + 20 +--R +--R Type: Expression Integer +--E 60 + +--S 61 of 139 +yx:=solve(ode172,y,x) +--R +--R +--R 11 2 9 +--R (7x - 11x )y(x) + 35x + 44 +--R (61) -------------------------------- +--R 11 2 9 +--R (36x - 36x )y(x) + 180x + 144 +--R Type: Union(Expression Integer,...) +--E 61 + +--S 62 of 139 +ode172expr := x**3*D(yx,x) - x**4*yx**2 + x**2*yx + 20 +--R +--R +--R (62) +--R 14 , +--R - 1296x y (x) +--R +--R + +--R 26 24 22 17 15 13 8 +--R - 49x + 252x + 25920x + 154x + 648x - 51840x - 121x +--R + +--R 6 4 +--R 396x + 25920x +--R * +--R 2 +--R y(x) +--R + +--R 24 22 20 15 13 11 6 +--R - 490x + 2520x + 259200x + 154x - 1944x - 51840x + 968x +--R + +--R 4 2 +--R - 3168x - 207360x +--R * +--R y(x) +--R + +--R 22 20 18 13 11 9 4 +--R - 1225x + 6300x + 648000x - 3080x - 12960x + 1036800x - 1936x +--R + +--R 2 +--R 6336x + 414720 +--R / +--R 22 13 4 2 20 11 2 +--R (1296x - 2592x + 1296x )y(x) + (12960x - 2592x - 10368x )y(x) +--R + +--R 18 9 +--R 32400x + 51840x + 20736 +--R Type: Expression Integer +--E 62 + +--S 63 of 139 +ode173 := x**3*D(y(x),x) - x**6*y(x)**2 - (2*x-3)*x**2*y(x) + 3 +--R +--R +--R 3 , 6 2 3 2 +--R (63) x y (x) - x y(x) + (- 2x + 3x )y(x) + 3 +--R +--R Type: Expression Integer +--E 63 + +--S 64 of 139 +yx:=solve(ode173,y,x) +--R +--R +--R 3 +--R - x y(x) + 1 +--R (64) ------------------ +--R 3 4x +--R (4x y(x) + 12)%e +--R Type: Union(Expression Integer,...) +--E 64 + +--S 65 of 139 +ode173expr := x**3*D(yx,x) - x**6*yx**2 - (2*x-3)*x**2*yx + 3 +--R +--R +--R (65) +--R 6 4x , 6 2 3 4x 2 +--R - 16x %e y (x) + (48x y(x) + 288x y(x) + 432)(%e ) +--R +--R + +--R 9 8 2 6 5 3 2 4x 12 2 +--R ((24x - 12x )y(x) + (48x - 72x )y(x) - 72x + 36x )%e - x y(x) +--R + +--R 9 6 +--R 2x y(x) - x +--R / +--R 6 2 3 4x 2 +--R (16x y(x) + 96x y(x) + 144)(%e ) +--R Type: Expression Integer +--E 65 + +--S 66 of 139 +ode174 := x*(x**2+1)*D(y(x),x) + x**2*y(x) +--R +--R +--R 3 , 2 +--R (66) (x + x)y (x) + x y(x) +--R +--R Type: Expression Integer +--E 66 + +--S 67 of 139 +ode174a:=solve(ode174,y,x) +--R +--R +--R 1 +--R (67) [particular= 0,basis= [---------]] +--R +------+ +--R | 2 +--R \|x + 1 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 67 + +--S 68 of 139 +yx:=ode174a.particular +--R +--R +--R (68) 0 +--R Type: Expression Integer +--E 68 + +--S 69 of 139 +ode174expr := x*(x**2+1)*D(yx,x) + x**2*yx +--R +--R +--R (69) 0 +--R Type: Expression Integer +--E 69 + +--S 70 of 139 +ode175 := x*(x**2-1)*D(y(x),x) - (2*x**2-1)*y(x) + a*x**3 +--R +--R +--R 3 , 2 3 +--R (70) (x - x)y (x) + (- 2x + 1)y(x) + a x +--R +--R Type: Expression Integer +--E 70 + +--S 71 of 139 +ode175a:=solve(ode175,y,x) +--R +--R +--R +------+ +--R | 2 +--R (71) [particular= a x,basis= [x\|x - 1 ]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 71 + +--S 72 of 139 +yx:=ode175a.particular +--R +--R +--R (72) a x +--R Type: Expression Integer +--E 72 + +--S 73 of 139 +ode175expr := x*(x**2-1)*D(yx,x) - (2*x**2-1)*yx + a*x**3 +--R +--R +--R (73) 0 +--R Type: Expression Integer +--E 73 + +--S 74 of 139 +ode176 := x*(x**2-1)*D(y(x),x) + (x**2-1)*y(x)**2 - x**2 +--R +--R +--R 3 , 2 2 2 +--R (74) (x - x)y (x) + (x - 1)y(x) - x +--R +--R Type: Expression Integer +--E 74 + +--S 75 of 139 +ode176a:=solve(ode176,y,x) +--R +--R +--R (75) "failed" +--R Type: Union("failed",...) +--E 75 + +--S 76 of 139 +ode177 := x**2*(x-1)*D(y(x),x) - y(x)**2 - x*(x-2)*y(x) +--R +--R +--R 3 2 , 2 2 +--R (76) (x - x )y (x) - y(x) + (- x + 2x)y(x) +--R +--R Type: Expression Integer +--E 76 + +--S 77 of 139 +yx:=solve(ode177,y,x) +--R +--R +--R 2 +--R - y(x) + x +--R (77) ----------- +--R (x - 1)y(x) +--R Type: Union(Expression Integer,...) +--E 77 + +--S 78 of 139 +ode177expr := x**2*(x-1)*D(yx,x) - yx**2 - x*(x-2)*yx +--R +--R +--R 6 5 4 , 3 2 2 2 4 +--R (- x + 2x - x )y (x) + (2x - 4x + 2x - 1)y(x) + 2x y(x) - x +--R +--R (78) ----------------------------------------------------------------- +--R 2 2 +--R (x - 2x + 1)y(x) +--R Type: Expression Integer +--E 78 + +--S 79 of 139 +ode178 := 2*x*(x**2-1)*D(y(x),x) + 2*(x**2-1)*y(x)**2 _ + - (3*x**2-5)*y(x) + x**2 - 3 +--R +--R +--R 3 , 2 2 2 2 +--R (79) (2x - 2x)y (x) + (2x - 2)y(x) + (- 3x + 5)y(x) + x - 3 +--R +--R Type: Expression Integer +--E 79 + +--S 80 of 139 +yx:=solve(ode178,y,x) +--R +--R +--R +------+ x +---+ +--I | 2 ++ \|%CL +-+ +--I (- y(x) + 1)\|x - 1 | -------------- d%CL + \|x +--R ++ +--------+ +--R | 2 +--I %CL\|%CL - 1 +--R (80) ----------------------------------------------------- +--R +------+ +--R | 2 +--R (y(x) - 1)\|x - 1 +--R Type: Union(Expression Integer,...) +--E 80 + +--S 81 of 139 +ode178expr := 2*x*(x**2-1)*D(yx,x) + 2*(x**2-1)*yx**2 _ + - (3*x**2-5)*yx + x**2 - 3 +--R +--R +--R (81) +--R +------+ +--R 2 2 2 2 +-+ | 2 +--R ((2x - 2)y(x) + (- 4x + 4)y(x) + 2x - 2)\|x \|x - 1 +--R * +--R x +---+ 2 +--I ++ \|%CL +--I | -------------- d%CL +--R ++ +--------+ +--R | 2 +--I %CL\|%CL - 1 +--R + +--R +------+ +--R 2 2 2 2 +-+ | 2 +--R ((3x - 5)y(x) + (- 6x + 10)y(x) + 3x - 5)\|x \|x - 1 +--R + +--R 3 3 +--R (- 4x + 4x)y(x) + 4x - 4x +--R * +--R x +---+ +--I ++ \|%CL +--I | -------------- d%CL +--R ++ +--------+ +--R | 2 +--I %CL\|%CL - 1 +--R + +--R 4 2 , +--R (- 2x + 2x )y (x) +--R +--R + +--R +------+ +--R 2 2 2 2 +-+ | 2 +--R ((x - 3)y(x) + (- 2x + 6)y(x) + x + 2x - 3)\|x \|x - 1 +--R + +--R 3 2 3 +--R (- 2x + 2x)y(x) + 2x - 2x +--R / +--R +------+ +--R 2 +-+ | 2 +--R (y(x) - 2y(x) + 1)\|x \|x - 1 +--R Type: Expression Integer +--E 81 + +--S 82 of 139 +ode179 := 3*x*(x**2-1)*D(y(x),x) + x*y(x)**2 - (x**2+1)*y(x) - 3*x +--R +--R +--R 3 , 2 2 +--R (82) (3x - 3x)y (x) + x y(x) + (- x - 1)y(x) - 3x +--R +--R Type: Expression Integer +--E 82 + +--S 83 of 139 +ode179a:=solve(ode179,y,x) +--R +--R +--R (83) "failed" +--R Type: Union("failed",...) +--E 83 + +--S 84 of 139 +ode180 := (a*x**2+b*x+c)*(x*D(y(x),x)-y(x)) - y(x)**2 + x**2 +--R +--R +--R 3 2 , 2 2 2 +--R (84) (a x + b x + c x)y (x) - y(x) + (- a x - b x - c)y(x) + x +--R +--R Type: Expression Integer +--E 84 + +--S 85 of 139 random generation, FAILURE OK. +yx:=solve(ode180,y,x) +--R +--R WARNING (genufact): No known algorithm to factor +--R 2 2 +--R 4 - 4a c + 2b 2 b +--R ? + ------------ ? - -----------, trying square-free. +--R 3 2 2 5 4 2 +--R 4a c - a b 4a c - a b +--R WARNING (genufact): No known algorithm to factor +--R 2 2 2 2 +--R 4 - 4a c + 2b - 4a b + 4a 2 - b + 4a b - 4a +--R ? + ------------------------- ? + -----------------, trying square-free. +--R 3 2 2 5 4 2 +--R 4a c - a b 4a c - a b +--R WARNING (genufact): No known algorithm to factor +--R 2 4 2 +--R 9 9b 8 (144a b - 24a)c - 36b + 12b 7 +--R ? - -- ? + ------------------------------ ? +--R a 3 2 2 +--R 4a c - a b +--R + +--R 3 5 3 +--R (- 336a b + 168a b)c + 84b - 84b 6 +--R ----------------------------------- ? +--R 4 3 2 +--R 4a c - a b +--R + +--R 2 4 2 2 2 2 +--R (2016a b - 2016a b + 144a )c +--R + +--R 6 4 2 8 6 4 +--R (- 1008a b + 1512a b - 192a b )c + 126b - 252b + 48b +--R / +--R 6 2 5 2 4 4 +--R 16a c - 8a b c + a b +--R * +--R 5 +--R ? +--R + +--R 2 5 2 3 2 2 +--R (- 2016a b + 3360a b - 720a b)c +--R + +--R 7 5 3 9 7 5 +--R (1008a b - 2520a b + 960a b )c - 126b + 420b - 240b +--R / +--R 7 2 6 2 5 4 +--R 16a c - 8a b c + a b +--R * +--R 4 +--R ? +--R + +--R 3 6 3 4 3 2 3 3 +--R (5376a b - 13440a b + 5760a b - 256a )c +--R + +--R 2 8 2 6 2 4 2 2 2 +--R (- 4032a b + 13440a b - 9120a b + 640a b )c +--R + +--R 10 8 6 4 12 10 +--R (1008a b - 4200a b + 3840a b - 384a b )c - 84b + 420b +--R + +--R 8 6 +--R - 480b + 64b +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 64a c - 48a b c + 12a b c - a b +--R * +--R 3 +--R ? +--R + +--R 3 7 3 5 3 3 3 3 +--R (- 2304a b + 8064a b - 5760a b + 768a b)c +--R + +--R 2 9 2 7 2 5 2 3 2 +--R (1728a b - 8064a b + 9120a b - 1920a b )c +--R + +--R 11 9 7 5 13 11 +--R (- 432a b + 2520a b - 3840a b + 1152a b )c + 36b - 252b +--R + +--R 9 7 +--R 480b - 192b +--R / +--R 10 3 9 2 2 8 4 7 6 +--R 64a c - 48a b c + 12a b c - a b +--R * +--R 2 +--R ? +--R + +--R 3 8 3 6 3 4 3 2 3 +--R (576a b - 2688a b + 2880a b - 768a b )c +--R + +--R 2 10 2 8 2 6 2 4 2 2 2 +--R (- 432a b + 2688a b - 4560a b + 1920a b - 256a b )c +--R + +--R 12 10 8 6 14 12 +--R (108a b - 840a b + 1920a b - 1152a b )c - 9b + 84b +--R + +--R 10 8 +--R - 240b + 192b +--R / +--R 11 3 10 2 2 9 4 8 6 +--R 64a c - 48a b c + 12a b c - a b +--R * +--R ? +--R + +--R 3 9 3 7 3 5 3 3 3 +--R (- 64a b + 384a b - 576a b + 256a b )c +--R + +--R 2 11 2 9 2 7 2 5 2 3 2 +--R (48a b - 384a b + 912a b - 640a b + 256a b )c +--R + +--R 13 11 9 7 15 13 11 +--R (- 12a b + 120a b - 384a b + 384a b )c + b - 12b + 48b +--R + +--R 9 +--R - 64b +--R / +--R 12 3 11 2 2 10 4 9 6 +--R 64a c - 48a b c + 12a b c - a b +--R , trying square-free. +--R WARNING (genufact): No known algorithm to factor +--R 9 9b - 18a 8 +--R ? + -------- ? +--R a +--R + +--R 2 2 3 4 3 +--R (144a b - 576a b + 576a - 24a)c - 36b + 144a b +--R + +--R 2 2 2 +--R (- 144a + 12)b - 24a b + 24a +--R / +--R 3 2 2 +--R 4a c - a b +--R * +--R 7 +--R ? +--R + +--R 3 2 2 3 4 2 5 +--R (336a b - 2016a b + (4032a - 168a)b - 2688a + 336a )c - 84b +--R + +--R 4 2 3 3 2 2 3 +--R 504a b + (- 1008a + 84)b + (672a - 336a)b + 504a b - 336a +--R / +--R 4 3 2 +--R 4a c - a b +--R * +--R 6 +--R ? +--R + +--R 2 4 3 3 4 2 2 +--R 2016a b - 16128a b + (48384a - 2016a )b +--R + +--R 5 3 6 4 2 +--R (- 64512a + 8064a )b + 32256a - 8064a + 144a +--R * +--R 2 +--R c +--R + +--R 6 2 5 3 4 +--R - 1008a b + 8064a b + (- 24192a + 1512a)b +--R + +--R 4 2 3 5 3 2 +--R (32256a - 8064a )b + (- 16128a + 16128a - 192a)b +--R + +--R 4 2 5 3 +--R (- 16128a + 480a )b + 8064a - 480a +--R * +--R c +--R + +--R 8 7 2 6 3 5 +--R 126b - 1008a b + (3024a - 252)b + (- 4032a + 1512a)b +--R + +--R 4 2 4 3 3 4 2 2 +--R (2016a - 3528a + 48)b + (4032a - 192a)b + (- 2016a + 336a )b +--R + +--R 3 4 +--R - 288a b + 144a +--R / +--R 6 2 5 2 4 4 +--R 16a c - 8a b c + a b +--R * +--R 5 +--R ? +--R + +--R 2 5 3 4 4 2 3 +--R 2016a b - 20160a b + (80640a - 3360a )b +--R + +--R 5 3 2 6 4 2 +--R (- 161280a + 20160a )b + (161280a - 40320a + 720a )b +--R + +--R 7 5 3 +--R - 64512a + 26880a - 1440a +--R * +--R 2 +--R c +--R + +--R 7 2 6 3 5 +--R - 1008a b + 10080a b + (- 40320a + 2520a)b +--R + +--R 4 2 4 5 3 3 +--R (80640a - 18480a )b + (- 80640a + 53760a - 960a)b +--R + +--R 6 4 2 2 5 3 6 +--R (32256a - 80640a + 4320a )b + (67200a - 7200a )b - 26880a +--R + +--R 4 +--R 4800a +--R * +--R c +--R + +--R 9 8 2 7 3 6 +--R 126b - 1260a b + (5040a - 420)b + (- 10080a + 3360a)b +--R + +--R 4 2 5 5 3 4 +--R (10080a - 10920a + 240)b + (- 4032a + 18480a - 1440a)b +--R + +--R 4 2 3 5 3 2 4 5 +--R (- 16800a + 3600a )b + (6720a - 4800a )b + 3600a b - 1440a +--R / +--R 7 2 6 2 5 4 +--R 16a c - 8a b c + a b +--R * +--R 4 +--R ? +--R + +--R 3 6 4 5 5 3 4 +--R 5376a b - 64512a b + (322560a - 13440a )b +--R + +--R 6 4 3 7 5 3 2 +--R (- 860160a + 107520a )b + (1290240a - 322560a + 5760a )b +--R + +--R 8 6 4 9 7 +--R (- 1032192a + 430080a - 23040a )b + 344064a - 215040a +--R + +--R 5 3 +--R 23040a - 256a +--R * +--R 3 +--R c +--R + +--R 2 8 3 7 4 2 6 +--R - 4032a b + 48384a b + (- 241920a + 13440a )b +--R + +--R 5 3 5 6 4 2 4 +--R (645120a - 120960a )b + (- 967680a + 443520a - 9120a )b +--R + +--R 7 5 3 3 +--R (774144a - 860160a + 55680a )b +--R + +--R 8 6 4 2 2 +--R (- 258048a + 967680a - 132480a + 640a )b +--R + +--R 7 5 3 8 6 4 +--R (- 645120a + 153600a - 1792a )b + 215040a - 76800a + 1792a +--R * +--R 2 +--R c +--R + +--R 10 2 9 3 8 +--R 1008a b - 12096a b + (60480a - 4200a)b +--R + +--R 4 2 7 5 3 6 +--R (- 161280a + 40320a )b + (241920a - 161280a + 3840a)b +--R + +--R 6 4 2 5 +--R (- 193536a + 349440a - 27840a )b +--R + +--R 7 5 3 4 +--R (64512a - 443520a + 83520a - 384a)b +--R + +--R 6 4 2 3 +--R (322560a - 134400a + 1792a )b +--R + +--R 7 5 3 2 6 4 +--R (- 107520a + 124800a - 3584a )b + (- 69120a + 3584a )b +--R + +--R 7 5 +--R 23040a - 1792a +--R * +--R c +--R + +--R 12 11 2 10 3 9 +--R - 84b + 1008a b + (- 5040a + 420)b + (13440a - 4200a)b +--R + +--R 4 2 8 5 3 7 +--R (- 20160a + 17640a - 480)b + (16128a - 40320a + 3840a)b +--R + +--R 6 4 2 6 +--R (- 5376a + 53760a - 12960a + 64)b +--R + +--R 5 3 5 6 4 2 4 +--R (- 40320a + 24000a - 384a)b + (13440a - 26400a + 1024a )b +--R + +--R 5 3 3 6 4 2 5 6 +--R (17280a - 1536a )b + (- 5760a + 1408a )b - 768a b + 256a +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 64a c - 48a b c + 12a b c - a b +--R * +--R 3 +--R ? +--R + +--R 3 7 4 6 5 3 5 +--R 2304a b - 32256a b + (193536a - 8064a )b +--R + +--R 6 4 4 7 5 3 3 +--R (- 645120a + 80640a )b + (1290240a - 322560a + 5760a )b +--R + +--R 8 6 4 2 +--R (- 1548288a + 645120a - 34560a )b +--R + +--R 9 7 5 3 10 +--R (1032192a - 645120a + 69120a - 768a )b - 294912a +--R + +--R 8 6 4 +--R 258048a - 46080a + 1536a +--R * +--R 3 +--R c +--R + +--R 2 9 3 8 4 2 7 +--R - 1728a b + 24192a b + (- 145152a + 8064a )b +--R + +--R 5 3 6 6 4 2 5 +--R (483840a - 88704a )b + (- 967680a + 411264a - 9120a )b +--R + +--R 7 5 3 4 +--R (1161216a - 1048320a + 73920a )b +--R + +--R 8 6 4 2 3 +--R (- 774144a + 1612800a - 243840a + 1920a )b +--R + +--R 9 7 5 3 2 +--R (221184a - 1548288a + 418560a - 9216a )b +--R + +--R 8 6 4 9 7 5 +--R (903168a - 384000a + 16128a )b - 258048a + 153600a - 10752a +--R * +--R 2 +--R c +--R + +--R 11 2 10 3 9 +--R 432a b - 6048a b + (36288a - 2520a)b +--R + +--R 4 2 8 5 3 7 +--R (- 120960a + 29232a )b + (241920a - 145152a + 3840a)b +--R + +--R 6 4 2 6 +--R (- 290304a + 403200a - 35520a )b +--R + +--R 7 5 3 5 +--R (193536a - 685440a + 139200a - 1152a)b +--R + +--R 8 6 4 2 4 +--R (- 55296a + 725760a - 301440a + 7680a )b +--R + +--R 7 5 3 3 +--R (- 451584a + 393600a - 21504a )b +--R + +--R 8 6 4 2 7 5 +--R (129024a - 318720a + 32256a )b + (161280a - 26880a )b +--R + +--R 8 6 +--R - 46080a + 10752a +--R * +--R c +--R + +--R 13 12 2 11 3 10 +--R - 36b + 504a b + (- 3024a + 252)b + (10080a - 3024a)b +--R + +--R 4 2 9 5 3 8 +--R (- 20160a + 15624a - 480)b + (24192a - 45360a + 4800a)b +--R + +--R 6 4 2 7 +--R (- 16128a + 80640a - 20640a + 192)b +--R + +--R 7 5 3 6 +--R (4608a - 88704a + 49920a - 1536a)b +--R + +--R 6 4 2 5 7 5 3 4 +--R (56448a - 74400a + 5376a )b + (- 16128a + 70080a - 10752a )b +--R + +--R 6 4 3 7 5 2 6 7 +--R (- 40320a + 13440a )b + (11520a - 10752a )b + 5376a b - 1536a +--R / +--R 10 3 9 2 2 8 4 7 6 +--R 64a c - 48a b c + 12a b c - a b +--R * +--R 2 +--R ? +--R + +--R 3 8 4 7 5 3 6 +--R 576a b - 9216a b + (64512a - 2688a )b +--R + +--R 6 4 5 7 5 3 4 +--R (- 258048a + 32256a )b + (645120a - 161280a + 2880a )b +--R + +--R 8 6 4 3 +--R (- 1032192a + 430080a - 23040a )b +--R + +--R 9 7 5 3 2 +--R (1032192a - 645120a + 69120a - 768a )b +--R + +--R 10 8 6 4 11 +--R (- 589824a + 516096a - 92160a + 3072a )b + 147456a +--R + +--R 9 7 5 +--R - 172032a + 46080a - 3072a +--R * +--R 3 +--R c +--R + +--R 2 10 3 9 4 2 8 +--R - 432a b + 6912a b + (- 48384a + 2688a )b +--R + +--R 5 3 7 6 4 2 6 +--R (193536a - 34944a )b + (- 483840a + 196224a - 4560a )b +--R + +--R 7 5 3 5 +--R (774144a - 623616a + 46080a )b +--R + +--R 8 6 4 2 4 +--R (- 774144a + 1236480a - 195840a + 1920a )b +--R + +--R 9 7 5 3 3 +--R (442368a - 1591296a + 453120a - 13056a )b +--R + +--R 10 8 6 4 2 2 +--R (- 110592a + 1333248a - 610560a + 34560a - 256a )b +--R + +--R 9 7 5 3 10 +--R (- 688128a + 460800a - 43008a + 1024a )b + 172032a +--R + +--R 8 6 4 +--R - 153600a + 21504a - 1024a +--R * +--R 2 +--R c +--R + +--R 12 2 11 3 10 +--R 108a b - 1728a b + (12096a - 840a)b +--R + +--R 4 2 9 5 3 8 +--R (- 48384a + 11424a )b + (120960a - 67872a + 1920a)b +--R + +--R 6 4 2 7 +--R (- 193536a + 231168a - 21600a )b +--R + +--R 7 5 3 6 +--R (193536a - 497280a + 105120a - 1152a)b +--R + +--R 8 6 4 2 5 +--R (- 110592a + 698880a - 289920a + 9984a )b +--R + +--R 9 7 5 3 4 +--R (27648a - 634368a + 498240a - 36864a )b +--R + +--R 8 6 4 2 3 +--R (344064a - 552960a + 75264a + 512a )b +--R + +--R 9 7 5 3 2 +--R (- 86016a + 399360a - 91392a - 2560a )b +--R + +--R 8 6 4 9 7 5 +--R (- 184320a + 64512a + 4096a )b + 46080a - 21504a - 2048a +--R * +--R c +--R + +--R 14 13 2 12 3 11 +--R - 9b + 144a b + (- 1008a + 84)b + (4032a - 1176a)b +--R + +--R 4 2 10 5 3 9 +--R (- 10080a + 7224a - 240)b + (16128a - 25536a + 2880a)b +--R + +--R 6 4 2 8 +--R (- 16128a + 57120a - 15120a + 192)b +--R + +--R 7 5 3 7 +--R (9216a - 83328a + 45600a - 1920a)b +--R + +--R 8 6 4 2 6 +--R (- 2304a + 77952a - 87120a + 8448a )b +--R + +--R 7 5 3 5 +--R (- 43008a + 109440a - 21504a )b +--R + +--R 8 6 4 2 4 +--R (10752a - 90240a + 34944a - 256a )b +--R + +--R 7 5 3 3 8 6 4 2 +--R (46080a - 37632a + 1536a )b + (- 11520a + 26880a - 3328a )b +--R + +--R 7 5 8 6 +--R (- 12288a + 3072a )b + 3072a - 1024a +--R / +--R 11 3 10 2 2 9 4 8 6 +--R 64a c - 48a b c + 12a b c - a b +--R * +--R ? +--R + +--R 3 9 4 8 5 3 7 6 4 6 +--R 64a b - 1152a b + (9216a - 384a )b + (- 43008a + 5376a )b +--R + +--R 7 5 3 5 +--R (129024a - 32256a + 576a )b +--R + +--R 8 6 4 4 +--R (- 258048a + 107520a - 5760a )b +--R + +--R 9 7 5 3 3 +--R (344064a - 215040a + 23040a - 256a )b +--R + +--R 10 8 6 4 2 +--R (- 294912a + 258048a - 46080a + 1536a )b +--R + +--R 11 9 7 5 12 10 +--R (147456a - 172032a + 46080a - 3072a )b - 32768a + 49152a +--R + +--R 8 6 +--R - 18432a + 2048a +--R * +--R 3 +--R c +--R + +--R 2 11 3 10 4 2 9 +--R - 48a b + 864a b + (- 6912a + 384a )b +--R + +--R 5 3 8 6 4 2 7 +--R (32256a - 5760a )b + (- 96768a + 38016a - 912a )b +--R + +--R 7 5 3 6 +--R (193536a - 145152a + 11040a )b +--R + +--R 8 6 4 2 5 +--R (- 258048a + 354816a - 57600a + 640a )b +--R + +--R 9 7 5 3 4 +--R (221184a - 580608a + 168960a - 5632a )b +--R + +--R 10 8 6 4 2 3 +--R (- 110592a + 645120a - 303360a + 20224a - 256a )b +--R + +--R 11 9 7 5 3 2 +--R (24576a - 479232a + 336384a - 37376a + 1536a )b +--R + +--R 10 8 6 4 11 9 +--R (221184a - 215040a + 35840a - 3072a )b - 49152a + 61440a +--R + +--R 7 5 +--R - 14336a + 2048a +--R * +--R 2 +--R c +--R + +--R 13 2 12 3 11 4 2 10 +--R 12a b - 216a b + (1728a - 120a)b + (- 8064a + 1872a )b +--R + +--R 5 3 9 6 4 2 8 +--R (24192a - 12960a + 384a)b + (- 48384a + 52416a - 5088a )b +--R + +--R 7 5 3 7 +--R (64512a - 137088a + 29664a - 384a)b +--R + +--R 8 6 4 2 6 +--R (- 55296a + 241920a - 100032a + 4096a )b +--R + +--R 9 7 5 3 5 +--R (27648a - 290304a + 215616a - 18944a )b +--R + +--R 10 8 6 4 2 4 +--R (- 6144a + 230400a - 309888a + 49664a + 512a )b +--R + +--R 9 7 5 3 3 +--R (- 110592a + 301056a - 80640a - 3584a )b +--R + +--R 10 8 6 4 2 +--R (24576a - 196608a + 82432a + 9216a )b +--R + +--R 9 7 5 10 8 6 +--R (82944a - 50176a - 10240a )b - 18432a + 14336a + 4096a +--R * +--R c +--R + +--R 15 14 2 13 3 12 +--R - b + 18a b + (- 144a + 12)b + (672a - 192a)b +--R + +--R 4 2 11 5 3 10 +--R (- 2016a + 1368a - 48)b + (4032a - 5712a + 672a)b +--R + +--R 6 4 2 9 +--R (- 5376a + 15456a - 4176a + 64)b +--R + +--R 7 5 3 8 +--R (4608a - 28224a + 15168a - 768a)b +--R + +--R 8 6 4 2 7 +--R (- 2304a + 34944a - 35664a + 4096a )b +--R + +--R 9 7 5 3 6 +--R (512a - 28416a + 56736a - 12800a )b +--R + +--R 8 6 4 2 5 +--R (13824a - 61824a + 25984a - 256a )b +--R + +--R 9 7 5 3 4 +--R (- 3072a + 45312a - 35840a + 2048a )b +--R + +--R 8 6 4 3 9 7 5 2 +--R (- 20736a + 34048a - 6400a )b + (4608a - 22016a + 9728a )b +--R + +--R 8 6 9 7 +--R (9216a - 7168a )b - 2048a + 2048a +--R / +--R 12 3 11 2 2 10 4 9 6 +--R 64a c - 48a b c + 12a b c - a b +--R , trying square-free. +--R +--R (85) +--R - y(x) + x +--R / +--R (2y(x) + 2x) +--R * +--R %e +--R ** +--R 2 +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b + (8a c - 2a b )x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Union(Expression Integer,...) +--E 85 + +--S 86 of 139 +ode180expr := (a*x**2+b*x+c)*(x*D(yx,x)-yx) - yx**2 + x**2 +--R +--R +--R (86) +--R 2 2 3 4 +--R (4x y(x) + 8x y(x) + 4x ) +--R * +--R %e +--R ** +--R 2 +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b +--R + +--R 2 2 3 +--R (8a c - 2a b )x + 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R ** +--R 2 +--R + +--R 4 3 2 , 2 2 +--R (- 4a x - 4b x - 4c x )y (x) + (2a x + (2b + 4)x + 2c)y(x) +--R +--R + +--R 3 2 4 3 2 +--R (4a x + 4b x + 4c x)y(x) - 2a x + (- 2b - 4)x - 2c x +--R * +--R %e +--R ** +--R 2 +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b +--R + +--R 2 2 3 +--R (8a c - 2a b )x + 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 +--R - y(x) + 2x y(x) - x +--R / +--R 2 2 +--R (4y(x) + 8x y(x) + 4x ) +--R * +--R %e +--R ** +--R 2 +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 +--R (2a x + 2a b x - 2a c + b )\|- 4a c + b +--R + +--R 2 2 3 +--R (8a c - 2a b )x + 4a b c - b +--R / +--R 2 +--R a x + b x + c +--R / +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R ** +--R 2 +--R Type: Expression Integer +--E 86 + +--S 87 of 139 +ode181 := x**4*(D(y(x),x)+y(x)**2) + a +--R +--R +--R 4 , 4 2 +--R (87) x y (x) + x y(x) + a +--R +--R Type: Expression Integer +--E 87 + +--S 88 of 139 +yx:=solve(ode181,y,x) +--R +--R 2 +--R WARNING (genufact): No known algorithm to factor ? + a, trying square-free. +--R +--R +---+ 2 +--R \|- a - x y(x) + x +--R (88) ------------------------------------ +--R +---+ +--R 2\|- a +--R ------- +--R 2 +---+ x +--R ((2x y(x) - 2x)\|- a - 2a)%e +--R Type: Union(Expression Integer,...) +--E 88 + +--S 89 of 139 +ode181expr := x**4*(D(yx,x)+yx**2) + a +--R +--R +--R (89) +--R +---+ +--R 2\|- a +--R ------- +--R 6 x , +--R - 4a x %e y (x) +--R +--R + +--R 2 2 2 +---+ 2 4 2 2 3 2 2 3 +--R ((8a x y(x) - 8a x)\|- a + 4a x y(x) - 8a x y(x) + 4a x - 4a ) +--R * +--R +---+ 2 +--R 2\|- a +--R ------- +--R x +--R (%e ) +--R + +--R +---+ +--R 2\|- a +--R ------- +--R 6 2 2 2 x 6 5 +---+ 8 2 +--R (- 4a x y(x) - 4a x )%e + (2x y(x) - 2x )\|- a - x y(x) +--R + +--R 7 6 4 +--R 2x y(x) - x + a x +--R / +--R 2 +---+ 4 2 3 2 2 +--R ((8a x y(x) - 8a x)\|- a + 4a x y(x) - 8a x y(x) + 4a x - 4a ) +--R * +--R +---+ 2 +--R 2\|- a +--R ------- +--R x +--R (%e ) +--R Type: Expression Integer +--E 89 + +--S 90 of 139 +ode182 := x*(x**3-1)*D(y(x),x) - 2*x*y(x)**2 + y(x) + x**2 +--R +--R +--R 4 , 2 2 +--R (90) (x - x)y (x) - 2x y(x) + y(x) + x +--R +--R Type: Expression Integer +--E 90 +@ + +This never completes +\begin{verbatim} + ode182a:=solve(ode182,y,x) +\end{verbatim} +<<*>>= + +--S 91 of 139 +ode183 := (2*x**4-x)*D(y(x),x) - 2*(x**3-1)*y(x) +--R +--R +--R 4 , 3 +--R (91) (2x - x)y (x) + (- 2x + 2)y(x) +--R +--R Type: Expression Integer +--E 91 + +--S 92 of 139 +ode183a:=solve(ode183,y,x) +--R +--R +--R 2 +--R x +--R (92) [particular= 0,basis= [----------]] +--R +-------+ +--R 3| 3 +--R \|2x - 1 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 92 + +--S 93 of 139 +yx:=ode183a.particular +--R +--R +--R (93) 0 +--R Type: Expression Integer +--E 93 + +--S 94 of 139 +ode183expr := (2*x**4-x)*D(yx,x) - 2*(x**3-1)*yx +--R +--R +--R (94) 0 +--R Type: Expression Integer +--E 94 + +--S 95 of 139 +ode184 := (a*x**2+b*x+c)**2*(D(y(x),x)+y(x)**2) + A +--R +--R +--R (95) +--R 2 4 3 2 2 2 , +--R (a x + 2a b x + (2a c + b )x + 2b c x + c )y (x) +--R +--R + +--R 2 4 3 2 2 2 2 +--R (a x + 2a b x + (2a c + b )x + 2b c x + c )y(x) + A +--R Type: Expression Integer +--E 95 + +@ +This never completes +\begin{verbatim} + ode184a:=solve(ode184,y,x) +\end{verbatim} +<<*>>= + +--S 96 of 139 +ode185 := x**7*D(y(x),x) + 2*(x**2+1)*y(x)**3 + 5*x**3*y(x)**2 +--R +--R +--R 7 , 2 3 3 2 +--R (96) x y (x) + (2x + 2)y(x) + 5x y(x) +--R +--R Type: Expression Integer +--E 96 + +--S 97 of 139 +ode185a:=solve(ode185,y,x) +--R +--R +--R (97) "failed" +--R Type: Union("failed",...) +--E 97 + +--S 98 of 139 +ode186 := x**n*D(y(x),x) + y(x)**2 -(n-1)*x**(n-1)*y(x) + x**(2*n-2) +--R +--R +--R n , 2n - 2 n - 1 2 +--R (98) x y (x) + x + (- n + 1)y(x)x + y(x) +--R +--R Type: Expression Integer +--E 98 + +--S 99 of 139 +ode186a:=solve(ode186,y,x) +--R +--R +--R (99) "failed" +--R Type: Union("failed",...) +--E 99 + +--S 100 of 139 +ode187 := x**n*D(y(x),x) - a*y(x)**2 - b*x**(2*n-2) +--R +--R +--R n , 2n - 2 2 +--R (100) x y (x) - b x - a y(x) +--R +--R Type: Expression Integer +--E 100 + +--S 101 of 139 +ode187a:=solve(ode187,y,x) +--R +--R +--R (101) "failed" +--R Type: Union("failed",...) +--E 101 + +--S 102 of 139 +ode188 := x**(2*n+1)*D(y(x),x) - a*y(x)**3 - b*x**3*n +--R +--R +--R 2n + 1 , 3 3 +--R (102) x y (x) - a y(x) - b n x +--R +--R Type: Expression Integer +--E 102 + +--S 103 of 139 +ode188a:=solve(ode188,y,x) +--R +--R +--R (103) "failed" +--R Type: Union("failed",...) +--E 103 + +--S 104 of 139 +ode189 := x**(m*(n-1)+n)*D(y(x),x) - a*y(x)**n - b*x**(n*(m+1)) +--R +--R +--R (m + 1)n - m , n (m + 1)n +--R (104) x y (x) - a y(x) - b x +--R +--R Type: Expression Integer +--E 104 + +--S 105 of 139 +ode189a:=solve(ode189,y,x) +--R +--R +--R (105) "failed" +--R Type: Union("failed",...) +--E 105 + +--S 106 of 139 +ode190 := sqrt(x**2-1)*D(y(x),x) - sqrt(y(x)**2-1) +--R +--R +--R +------+ +---------+ +--R | 2 , | 2 +--R (106) \|x - 1 y (x) - \|y(x) - 1 +--R +--R Type: Expression Integer +--E 106 + +--S 107 of 139 +ode190a:=solve(ode190,y,x) +--R +--R +--R (107) "failed" +--R Type: Union("failed",...) +--E 107 + +--S 108 of 139 +ode191 := sqrt(1-x**2)*D(y(x),x) - y(x)*sqrt(y(x)**2-1) +--R +--R +--R +--------+ +---------+ +--R | 2 , | 2 +--R (108) \|- x + 1 y (x) - y(x)\|y(x) - 1 +--R +--R Type: Expression Integer +--E 108 + +--S 109 of 139 +ode191a:=solve(ode191,y,x) +--R +--R +--R (109) "failed" +--R Type: Union("failed",...) +--E 109 + +--S 110 of 139 +ode192 := sqrt(x**2+a**2)*D(y(x),x) + y(x) - sqrt(x**2+a**2) + x +--R +--R +--R +-------+ +-------+ +--R | 2 2 , | 2 2 +--R (110) \|x + a y (x) - \|x + a + y(x) + x +--R +--R Type: Expression Integer +--E 110 + +--S 111 of 139 +ode192a:=solve(ode192,y,x) +--R +--R +--R (111) +--R +-------+ +-------+ +-------+ +--R | 2 2 | 2 2 | 2 2 +--R [particular= (- \|x + a + x)log(\|x + a - x),basis= [\|x + a - x]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 111 + +--S 112 of 139 +yx:=ode192a.particular +--R +--R +--R +-------+ +-------+ +--R | 2 2 | 2 2 +--R (112) (- \|x + a + x)log(\|x + a - x) +--R Type: Expression Integer +--E 112 + +--S 113 of 139 +ode192expr := sqrt(x**2+a**2)*D(yx,x) + yx - sqrt(x**2+a**2) + x +--R +--R +--R (113) 0 +--R Type: Expression Integer +--E 113 + +--S 114 of 139 +ode193 := x*D(y(x),x)*log(x) + y(x) - a*x*(log(x)+1) +--R +--R +--R , +--R (114) x log(x)y (x) - a x log(x) + y(x) - a x +--R +--R Type: Expression Integer +--E 114 + +--S 115 of 139 +ode193a:=solve(ode193,y,x) +--R +--R +--R 1 +--R (115) [particular= a x,basis= [------]] +--R log(x) +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 115 + +--S 116 of 139 +yx:=ode193a.particular +--R +--R (116) a x +--R Type: Expression Integer +--E 116 + +--S 117 of 139 +ode193expr := x*D(yx,x)*log(x) + yx - a*x*(log(x)+1) +--R +--R (117) 0 +--R Type: Expression Integer +--E 117 + +--S 118 of 139 +ode194 := x*D(y(x),x)*log(x) - y(x)**2*log(x) - _ + (2*log(x)**2+1)*y(x) - log(x)**3 +--R +--R +--R , 3 2 2 +--R (118) x log(x)y (x) - log(x) - 2y(x)log(x) - y(x) log(x) - y(x) +--R +--R Type: Expression Integer +--E 118 + +--S 119 of 139 +ode194a:=solve(ode194,y,x) +--R +--R +--R (119) "failed" +--R Type: Union("failed",...) +--E 119 + +--S 120 of 139 +ode195 := sin(x)*D(y(x),x) - y(x)**2*sin(x)**2 + (cos(x) - 3*sin(x))*y(x) + 4 +--R +--R +--R , 2 2 +--R (120) sin(x)y (x) - y(x) sin(x) - 3y(x)sin(x) + y(x)cos(x) + 4 +--R +--R Type: Expression Integer +--E 120 + +--S 121 of 139 +yx:=solve(ode195,y,x) +--R +--R +--R - y(x)sin(x) + 1 +--R (121) ------------------------ +--R 5x 5x +--R 5y(x)%e sin(x) + 20%e +--R Type: Union(Expression Integer,...) +--E 121 + +--S 122 of 139 +ode195expr:=sin(x)*D(yx,x) - yx**2*sin(x)**2 + (cos(x) - 3*sin(x))*yx + 4 +--R +--R +--R (122) +--R 5x 2 , 2 4 2 5x 3 +--R - 25%e sin(x) y (x) - y(x) sin(x) + (40y(x) %e + 2y(x))sin(x) +--R +--R + +--R 2 5x 2 2 5x 2 +--R (100y(x) (%e ) + (- 5y(x) cos(x) + 120y(x))%e - 1)sin(x) +--R + +--R 5x 2 5x 5x 2 +--R (800y(x)(%e ) + (- 40y(x)cos(x) - 160)%e )sin(x) + 1600(%e ) +--R + +--R 5x +--R 20cos(x)%e +--R / +--R 2 5x 2 2 5x 2 5x 2 +--R 25y(x) (%e ) sin(x) + 200y(x)(%e ) sin(x) + 400(%e ) +--R Type: Expression Integer +--E 122 + +--S 123 of 139 +ode196 := cos(x)*D(y(x),x) + y(x) + (1 + sin(x))*cos(x) +--R +--R +--R , +--R (123) cos(x)y (x) + cos(x)sin(x) + cos(x) + y(x) +--R +--R Type: Expression Integer +--E 123 + +--S 124 of 139 +ode196a:=solve(ode196,y,x) +--R +--R +--R (124) +--R [ +--R particular = +--R sin(x) - cos(x) - 1 +--R (- 4sin(x) + 4cos(x) + 4)log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2sin(x) - 2cos(x) - 2)log(----------) - sin(x) + (cos(x) + 1)sin(x) +--R cos(x) + 1 +--R / +--R sin(x) + cos(x) + 1 +--R , +--R sin(x) - cos(x) - 1 +--R basis= [-------------------]] +--R sin(x) + cos(x) + 1 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 124 + +--S 125 of 139 +yx:=ode196a.particular +--R +--R +--R (125) +--R sin(x) - cos(x) - 1 +--R (- 4sin(x) + 4cos(x) + 4)log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2sin(x) - 2cos(x) - 2)log(----------) - sin(x) + (cos(x) + 1)sin(x) +--R cos(x) + 1 +--R / +--R sin(x) + cos(x) + 1 +--R Type: Expression Integer +--E 125 + +--S 126 of 139 +ode196expr := cos(x)*D(yx,x) + yx + (1 + sin(x))*cos(x) +--R +--R +--R (126) +--R 2 2 4 3 2 +--R (- 8cos(x) - 12cos(x) - 4)sin(x) - 8cos(x) - 12cos(x) + 4cos(x) +--R + +--R 12cos(x) + 4 +--R * +--R sin(x) - cos(x) - 1 +--R log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 4 3 2 +--R (4cos(x) + 6cos(x) + 2)sin(x) + 4cos(x) + 6cos(x) - 2cos(x) +--R + +--R - 6cos(x) - 2 +--R * +--R 2 +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 3 3 2 +--R (- cos(x) - 4cos(x) - 1)sin(x) + (cos(x) - cos(x))sin(x) +--R + +--R 4 3 5 3 +--R (- cos(x) - 4cos(x) + 4cos(x) + 1)sin(x) + cos(x) - 2cos(x) + cos(x) +--R / +--R 2 2 3 2 +--R (cos(x) + 1)sin(x) + (2cos(x) + 4cos(x) + 2)sin(x) + cos(x) + 3cos(x) +--R + +--R 3cos(x) + 1 +--R Type: Expression Integer +--E 126 + +--S 127 of 139 +ode197 := cos(x)*D(y(x),x) - y(x)**4 - y(x)*sin(x) +--R +--R +--R , 4 +--R (127) cos(x)y (x) - y(x)sin(x) - y(x) +--R +--R Type: Expression Integer +--E 127 + +--S 128 of 139 +yx:=solve(ode197,y,x) +--R +--R +--R 3 2 3 +--R (2y(x) cos(x) + y(x) )sin(x) + 1 +--R (128) --------------------------------- +--R 3 3 +--R y(x) cos(x) +--R Type: Union(Expression Integer,...) +--E 128 + +--S 129 of 139 +ode197expr := cos(x)*D(yx,x) - yx**4 - yx*sin(x) +--R +--R +--R (129) +--R 8 10 , +--R - 3y(x) cos(x) y (x) +--R +--R + +--R 12 8 12 6 12 4 +--R - 16y(x) cos(x) - 32y(x) cos(x) - 24y(x) cos(x) +--R + +--R 12 2 12 +--R - 8y(x) cos(x) - y(x) +--R * +--R 4 +--R sin(x) +--R + +--R 9 6 9 4 9 2 9 3 +--R (- 32y(x) cos(x) - 48y(x) cos(x) - 24y(x) cos(x) - 4y(x) )sin(x) +--R + +--R 12 9 6 4 6 2 6 2 +--R (2y(x) cos(x) - 24y(x) cos(x) - 24y(x) cos(x) - 6y(x) )sin(x) +--R + +--R 9 9 3 2 3 12 13 +--R (2y(x) cos(x) - 8y(x) cos(x) - 4y(x) )sin(x) + 2y(x) cos(x) +--R + +--R 12 11 +--R y(x) cos(x) - 1 +--R / +--R 12 12 +--R y(x) cos(x) +--R Type: Expression Integer +--E 129 + +--S 130 of 139 +ode198 := sin(x)*cos(x)*D(y(x),x) - y(x) - sin(x)**3 +--R +--R +--R , 3 +--R (130) cos(x)sin(x)y (x) - sin(x) - y(x) +--R +--R Type: Expression Integer +--E 130 + +--S 131 of 139 +ode198a:=solve(ode198,y,x) +--R +--R +--R sin(x) +--R (131) [particular= - sin(x),basis= [------]] +--R cos(x) +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 131 + +--S 132 of 139 +yx:=ode198a.particular +--R +--R +--R (132) - sin(x) +--R Type: Expression Integer +--E 132 + +--S 133 of 139 +ode198expr := sin(x)*cos(x)*D(yx,x) - yx - sin(x)**3 +--R +--R +--R 3 2 +--R (133) - sin(x) + (- cos(x) + 1)sin(x) +--R Type: Expression Integer +--E 133 + +--S 134 of 139 +ode199 := sin(2*x)*D(y(x),x) + sin(2*y(x)) +--R +--R +--R , +--R (134) sin(2x)y (x) + sin(2y(x)) +--R +--R Type: Expression Integer +--E 134 + +--S 135 of 139 +ode199a:=solve(ode199,y,x) +--R +--R +--R (135) "failed" +--R Type: Union("failed",...) +--E 135 + +--S 136 of 139 +ode200 := (a*sin(x)**2+b)*D(y(x),x) + a*y(x)*sin(2*x) + A*x*(a*sin(x)**2+c) +--R +--R +--R 2 , 2 +--R (136) (a sin(x) + b)y (x) + a y(x)sin(2x) + A a x sin(x) + A c x +--R +--R Type: Expression Integer +--E 136 + +--S 137 of 139 +ode200a:=solve(ode200,y,x) +--R +--R +--R (137) +--R 2 2 +--R - 2A a x cos(x)sin(x) - A a cos(x) + (2A c + A a)x +--R [particular= ----------------------------------------------------, +--R 2 +--R 4a cos(x) - 4b - 4a +--R 1 +--R basis= [-----------------]] +--R 2 +--R a cos(x) - b - a +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 137 + +--S 138 of 139 +yx:=ode200a.particular +--R +--R +--R 2 2 +--R - 2A a x cos(x)sin(x) - A a cos(x) + (2A c + A a)x +--R (138) ---------------------------------------------------- +--R 2 +--R 4a cos(x) - 4b - 4a +--R Type: Expression Integer +--E 138 + +--S 139 of 139 +ode200expr := (a*sin(x)**2+b)*D(yx,x) + a*yx*sin(2*x) + A*x*(a*sin(x)**2+c) +--R +--R +--R (139) +--R 3 3 2 3 3 4 +--R (- 2A a x cos(x) + (2A a b + 2A a )x cos(x))sin(x) - A a cos(x) +--R + +--R 2 3 2 2 3 2 +--R ((2A a c + A a )x + A a b + A a )cos(x) +--R + +--R 2 2 3 2 +--R ((- 2A a b - 2A a )c - A a b - A a )x +--R * +--R sin(2x) +--R + +--R 3 2 2 3 4 +--R (- 2A a x cos(x) + (- 2A a b - 2A a )x)sin(x) +--R + +--R 3 3 2 3 2 3 +--R (- 2A a cos(x) + (4A a c + 2A a )x cos(x))sin(x) +--R + +--R 3 4 2 2 3 2 +--R 2A a x cos(x) + (4A a c - 8A a b - 4A a )x cos(x) +--R + +--R 2 2 2 3 +--R ((- 4A a b - 4A a )c + 2A a b + 4A a b + 2A a )x +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 +--R (- 2A a b cos(x) + (4A a b c + 2A a b)x cos(x))sin(x) +--R + +--R 2 2 4 +--R (4A a c - 2A a b)x cos(x) +--R + +--R 2 2 2 2 +--R ((- 4A a b - 8A a )c + 2A a b + 4A a b)x cos(x) +--R + +--R 2 2 2 +--R ((4A a b + 4A a )c - 2A a b - 2A a b)x +--R / +--R 2 4 2 2 2 2 +--R 4a cos(x) + (- 8a b - 8a )cos(x) + 4b + 8a b + 4a +--R Type: Expression Integer +--E 139 + +)spool +)lisp (bye) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} {\bf http://www.cs.uwaterloo.ca/$\tilde{}$ecterrab/odetools.html} +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/kamke3.input.pdf b/src/axiom-website/CATS/kamke3.input.pdf new file mode 100644 index 0000000..3a30466 Binary files /dev/null and b/src/axiom-website/CATS/kamke3.input.pdf differ diff --git a/src/axiom-website/CATS/kamke4.input.pamphlet b/src/axiom-website/CATS/kamke4.input.pamphlet new file mode 100644 index 0000000..57e395d --- /dev/null +++ b/src/axiom-website/CATS/kamke4.input.pamphlet @@ -0,0 +1,1462 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input kamke4.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This is the 201-250 of the Kamke test suite as published by +E. S. Cheb-Terrab\cite{1}. They have been rewritten using Axiom +syntax. Where possible we show that the particular solution actually +satisfies the original ordinary differential equation. +\end{abstract} +\eject +\tableofcontents +\eject +<<*>>= +)spool kamke4.output +)set break resume +)set mes auto off +)clear all +--S 1 of 127 +y:=operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 1 + +--S 2 of 127 +f:=operator 'f +--R +--R +--R (2) f +--R Type: BasicOperator +--E 2 + +--S 3 of 127 +f0:=operator 'f0 +--R +--R +--R (3) f0 +--R Type: BasicOperator +--E 3 + +--S 4 of 127 +f1:=operator 'f1 +--R +--R +--R (4) f1 +--R Type: BasicOperator +--E 4 + +--S 5 of 127 +f2:=operator 'f2 +--R +--R +--R (5) f2 +--R Type: BasicOperator +--E 5 + +--S 6 of 127 +g:=operator 'g +--R +--R +--R (6) g +--R Type: BasicOperator +--E 6 + +--S 7 of 127 +tg:=operator 'tg +--R +--R +--R (7) tg +--R Type: BasicOperator +--E 7 + +--S 8 of 127 +h:=operator 'h +--R +--R +--R (8) h +--R Type: BasicOperator +--E 8 + +--S 9 of 127 +ode201 := 2*f(x)*D(y(x),x)+2*f(x)*y(x)**2-D(f(x),x)*y(x)-2*f(x)**2 +--R +--R +--R , , 2 2 +--R (9) 2f(x)y (x) - y(x)f (x) + 2f(x)y(x) - 2f(x) +--R +--R Type: Expression Integer +--E 9 + +--S 10 of 127 +solve(ode201,y,x) +--R +--R +--R (10) "failed" +--R Type: Union("failed",...) +--E 10 + +--S 11 of 127 +ode202 := f(x)*D(y(x),x)+g(x)*tg(y(x))+h(x) +--R +--R +--R , +--R (11) f(x)y (x) + g(x)tg(y(x)) + h(x) +--R +--R Type: Expression Integer +--E 11 + +--S 12 of 127 +solve(ode202,y,x) +--R +--R +--R (12) "failed" +--R Type: Union("failed",...) +--E 12 + +--S 13 of 127 +ode203 := y(x)*D(y(x),x)+y(x)+x**3 +--R +--R +--R , 3 +--R (13) y(x)y (x) + y(x) + x +--R +--R Type: Expression Integer +--E 13 + +--S 14 of 127 +solve(ode203,y,x) +--R +--R +--R (14) "failed" +--R Type: Union("failed",...) +--E 14 + +--S 15 of 127 +ode204 := y(x)*D(y(x),x)+a*y(x)+x +--R +--R +--R , +--R (15) y(x)y (x) + a y(x) + x +--R +--R Type: Expression Integer +--E 15 + +--S 16 of 127 +solve(ode204,y,x) +--R +--R +--R (16) "failed" +--R Type: Union("failed",...) +--E 16 + +--S 17 of 127 +ode205 := y(x)*D(y(x),x)+a*y(x)+(a**2-1)/(4)*x+b*x**n +--R +--R +--R , n 2 +--R 4y(x)y (x) + 4b x + 4a y(x) + (a - 1)x +--R +--R (17) ---------------------------------------- +--R 4 +--R Type: Expression Integer +--E 17 + +--S 18 of 127 +solve(ode205,y,x) +--R +--R +--R (18) "failed" +--R Type: Union("failed",...) +--E 18 + +--S 19 of 127 +ode206 := y(x)*D(y(x),x)+a*y(x)+b*exp(x)-2*a +--R +--R +--R , x +--R (19) y(x)y (x) + b %e + a y(x) - 2a +--R +--R Type: Expression Integer +--E 19 + +--S 20 of 127 +solve(ode206,y,x) +--R +--R +--R (20) "failed" +--R Type: Union("failed",...) +--E 20 + +--S 21 of 127 +ode207 := y(x)*D(y(x),x)+y(x)**2+4*x*(x+1) +--R +--R +--R , 2 2 +--R (21) y(x)y (x) + y(x) + 4x + 4x +--R +--R Type: Expression Integer +--E 21 + +--S 22 of 127 +yx:=solve(ode207,y,x) +--R +--R +--R 2 2 2x +--R (y(x) + 4x )%e +--R (22) ----------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 22 + +--S 23 of 127 +ode207expr := yx*D(yx,x)+yx**2+4*x*(x+1) +--R +--R +--R (23) +--R 3 2 2x 2 , +--R (2y(x) + 8x y(x))(%e ) y (x) +--R +--R + +--R 4 2 2 4 3 2x 2 2 +--R (3y(x) + (24x + 8x)y(x) + 48x + 32x )(%e ) + 16x + 16x +--R / +--R 4 +--R Type: Expression Integer +--E 23 + +--S 24 of 127 +ode208 := y(x)*D(y(x),x)+a*y(x)**2-b*cos(x+c) +--R +--R +--R , 2 +--R (24) y(x)y (x) - b cos(x + c) + a y(x) +--R +--R Type: Expression Integer +--E 24 + +--S 25 of 127 +yx:=solve(ode208,y,x) +--R +--R +--R 2a x 2 2 2a x +--R - 2b %e sin(x + c) + (- 4a b cos(x + c) + (4a + 1)y(x) )%e +--R (25) ------------------------------------------------------------------ +--R 2 +--R 8a + 2 +--R Type: Union(Expression Integer,...) +--E 25 + +--S 26 of 127 +ode208expr := yx*D(yx,x)+a*yx**2-b*cos(x+c) +--R +--R +--R (26) +--R 2 2a x 2 +--R (- 16a - 4)b y(x)(%e ) sin(x + c) +--R + +--R 3 4 2 3 2a x 2 +--R ((- 32a - 8a)b y(x)cos(x + c) + (32a + 16a + 2)y(x) )(%e ) +--R * +--R , +--R y (x) +--R +--R + +--R 2 2a x 2 2 +--R 4a b (%e ) sin(x + c) +--R + +--R 2 2 3 2 2a x 2 +--R ((32a + 4)b cos(x + c) + (- 32a - 8a)b y(x) )(%e ) sin(x + c) +--R + +--R 3 2 2 4 2 2 +--R (48a + 8a)b cos(x + c) + (- 96a - 32a - 2)b y(x) cos(x + c) +--R + +--R 5 3 4 +--R (48a + 24a + 3a)y(x) +--R * +--R 2a x 2 +--R (%e ) +--R + +--R 4 2 +--R (- 64a - 32a - 4)b cos(x + c) +--R / +--R 4 2 +--R 64a + 32a + 4 +--R Type: Expression Integer +--E 26 + +--S 27 of 127 +ode209 := y(x)*D(y(x),x)-sqrt(a*y(x)**2+b) +--R +--R +--R +-----------+ +--R , | 2 +--R (27) y(x)y (x) - \|a y(x) + b +--R +--R Type: Expression Integer +--E 27 + +--S 28 of 127 +yx:=solve(ode209,y,x) +--R +--R +--R +-----------+ +--R +-+ | 2 2 +-+ +--R - x\|b \|a y(x) + b + y(x) \|b + b x +--R (28) --------------------------------------- +--R +-----------+ +--R +-+ | 2 +--R \|b \|a y(x) + b - b +--R Type: Union(Expression Integer,...) +--E 28 + +--S 29 of 127 +ode209expr := yx*D(yx,x)-sqrt(a*yx**2+b) +--R +--R +--R (29) +--R +-----------+ +--R 2 2 | 2 2 4 2 2 +-+ +--R ((- 3a b y(x) - 4b )\|a y(x) + b + (a y(x) + 5a b y(x) + 4b )\|b ) +--R * +--R ROOT +--R +-----------+ +--R 2 +-+ 2 | 2 2 +-+ +--R ((2a x + 2b)\|b + 2a x y(x) )\|a y(x) + b - 2a x y(x) \|b +--R + +--R 4 2 2 2 2 2 +--R - a y(x) + (- a x - a b)y(x) - 2a b x - 2b +--R / +--R +-----------+ +--R +-+ | 2 2 +--R 2\|b \|a y(x) + b - a y(x) - 2b +--R + +--R +-----------+ +--R 3 +-+ 3 | 2 +--R ((a x y(x) + 4b x y(x))\|b + 2b y(x) )\|a y(x) + b +--R + +--R 5 3 +-+ 3 2 +--R (- a y(x) - 2b y(x) )\|b - 3a b x y(x) - 4b x y(x) +--R * +--R , +--R y (x) +--R +--R + +--R +-----------+ +--R 4 2 +-+ 2 2 | 2 +--R ((a y(x) + 2b y(x) )\|b + 3a b x y(x) + 4b x)\|a y(x) + b +--R + +--R 2 4 2 2 +-+ 4 2 2 +--R (- a x y(x) - 5a b x y(x) - 4b x)\|b - 2a b y(x) - 2b y(x) +--R / +--R +-----------+ +--R 2 2 | 2 2 4 2 2 +-+ +--R (3a b y(x) + 4b )\|a y(x) + b + (- a y(x) - 5a b y(x) - 4b )\|b +--R Type: Expression Integer +--E 29 + +--S 30 of 127 +ode210 := y(x)*D(y(x),x)+x*y(x)**2-4*x +--R +--R +--R , 2 +--R (30) y(x)y (x) + x y(x) - 4x +--R +--R Type: Expression Integer +--E 30 + +--S 31 of 127 +yx:=solve(ode210,y,x) +--R +--R +--R 2 +--R 2 x +--R (y(x) - 4)%e +--R (31) --------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 31 + +--S 32 of 127 +ode210expr := yx*D(yx,x)+x*yx**2-4*x +--R +--R +--R (32) +--R 2 2 2 2 +--R 3 x , 4 2 x +--R (2y(x) - 8y(x))(%e ) y (x) + (3x y(x) - 24x y(x) + 48x)(%e ) - 16x +--R +--R ------------------------------------------------------------------------ +--R 4 +--R Type: Expression Integer +--E 32 + +--S 33 of 127 +ode211 := y(x)*D(y(x),x)-x*exp(x/y(x)) +--R +--R +--R x +--R ---- +--R , y(x) +--R (33) y(x)y (x) - x %e +--R +--R Type: Expression Integer +--E 33 + +--S 34 of 127 +solve(ode211,y,x) +--R +--R +--R (34) "failed" +--R Type: Union("failed",...) +--E 34 + +--S 35 of 127 +ode212 := y(x)*D(y(x),x)+f(x**2+y(x)**2)*g(x)+x +--R +--R +--R , 2 2 +--R (35) y(x)y (x) + g(x)f(y(x) + x ) + x +--R +--R Type: Expression Integer +--E 35 + +--S 36 of 127 +solve(ode212,y,x) +--R +--R +--R (36) "failed" +--R Type: Union("failed",...) +--E 36 + +--S 37 of 127 +ode213 := (y(x)+1)*D(y(x),x)-y(x)-x +--R +--R +--R , +--R (37) (y(x) + 1)y (x) - y(x) - x +--R +--R Type: Expression Integer +--E 37 + +--S 38 of 127 +solve(ode213,y,x) +--R +--R +--R (38) "failed" +--R Type: Union("failed",...) +--E 38 + +--S 39 of 127 +ode214 := (y(x)+x-1)*D(y(x),x)-y(x)+2*x+3 +--R +--R +--R , +--R (39) (y(x) + x - 1)y (x) - y(x) + 2x + 3 +--R +--R Type: Expression Integer +--E 39 + +--S 40 of 127 +solve(ode214,y,x) +--R +--R +--R (40) "failed" +--R Type: Union("failed",...) +--E 40 + +--S 41 of 127 +ode215 := (y(x)+2*x-2)*D(y(x),x)-y(x)+x+1 +--R +--R +--R , +--R (41) (y(x) + 2x - 2)y (x) - y(x) + x + 1 +--R +--R Type: Expression Integer +--E 41 + +--S 42 of 127 +solve(ode215,y,x) +--R +--R +--R (42) "failed" +--R Type: Union("failed",...) +--E 42 + +--S 43 of 127 +ode216 := (y(x)-2*x+1)*D(y(x),x)+y(x)+x +--R +--R +--R , +--R (43) (y(x) - 2x + 1)y (x) + y(x) + x +--R +--R Type: Expression Integer +--E 43 + +--S 44 of 127 +solve(ode216,y,x) +--R +--R +--R (44) "failed" +--R Type: Union("failed",...) +--E 44 + +--S 45 of 127 +ode217 := (y(x)-x**2)*D(y(x),x)-x +--R +--R +--R 2 , +--R (45) (y(x) - x )y (x) - x +--R +--R Type: Expression Integer +--E 45 + +--S 46 of 127 +yx:=solve(ode217,y,x) +--R +--R +--R 2 2y(x) +--R (2y(x) - 2x - 1)%e +--R (46) ------------------------ +--R 4 +--R Type: Union(Expression Integer,...) +--E 46 + +--S 47 of 127 +ode217expr := (yx-x**2)*D(yx,x)-x +--R +--R +--R (47) +--R 2 2 4 2 2y(x) 2 +--R (2y(x) + (- 4x - 1)y(x) + 2x + x )(%e ) +--R + +--R 2 4 2y(x) +--R (- 4x y(x) + 4x )%e +--R * +--R , +--R y (x) +--R +--R + +--R 3 2y(x) 2 3 2y(x) +--R (- 2x y(x) + 2x + x)(%e ) + 4x %e - 4x +--R / +--R 4 +--R Type: Expression Integer +--E 47 + +--S 48 of 127 +ode218 := (y(x)-x**2)*D(y(x),x)+4*x*y(x) +--R +--R +--R 2 , +--R (48) (y(x) - x )y (x) + 4x y(x) +--R +--R Type: Expression Integer +--E 48 + +--S 49 of 127 +yx:=solve(ode218,y,x) +--R +--R +--R 2 +--R 2y(x) + 2x +--R (49) ----------- +--R +----+ +--R \|y(x) +--R Type: Union(Expression Integer,...) +--E 49 + +--S 50 of 127 +ode218expr := (yx-x**2)*D(yx,x)+4*x*yx +--R +--R +--R (50) +--R 2 4 +----+ 2 2 4 , +--R ((2y(x) - 2x )\|y(x) - x y(x) + x y(x))y (x) +--R +--R + +--R 2 3 +----+ 3 3 2 +--R (8x y(x) + 8x y(x))\|y(x) + 8x y(x) + 4x y(x) +--R / +--R 2 +----+ +--R y(x) \|y(x) +--R Type: Expression Integer +--E 50 + +--S 51 of 127 +ode219 := (y(x)+g(x))*D(y(x),x)-f2(x)*y(x)**2-f1(x)*y(x)-f0(x) +--R +--R +--R , 2 +--R (51) (y(x) + g(x))y (x) - f2(x)y(x) - f1(x)y(x) - f0(x) +--R +--R Type: Expression Integer +--E 51 + +--S 52 of 127 +solve(ode219,y,x) +--R +--R +--R (52) "failed" +--R Type: Union("failed",...) +--E 52 + +--S 53 of 127 +ode220 := 2*y(x)*D(y(x),x)-x*y(x)**2-x**3 +--R +--R +--R , 2 3 +--R (53) 2y(x)y (x) - x y(x) - x +--R +--R Type: Expression Integer +--E 53 + +--S 54 of 127 +yx:=solve(ode220,y,x) +--R +--R +--R 2 +--R x +--R - -- +--R 2 2 2 +--R (54) (y(x) + x + 2)%e +--R Type: Union(Expression Integer,...) +--E 54 + +--S 55 of 127 +ode220expr := 2*yx*D(yx,x)-x*yx**2-x**3 +--R +--R +--R (55) +--R 2 2 +--R x +--R - -- +--R 3 2 2 , +--R (4y(x) + (4x + 8)y(x))(%e ) y (x) +--R +--R + +--R 2 2 +--R x +--R - -- +--R 4 3 2 5 3 2 3 +--R (- 3x y(x) + (- 6x - 8x)y(x) - 3x - 8x - 4x)(%e ) - x +--R Type: Expression Integer +--E 55 + +--S 56 of 127 +ode221 := (2*y(x)+x+1)*D(y(x),x)-(2*y(x)+x-1) +--R +--R +--R , +--R (56) (2y(x) + x + 1)y (x) - 2y(x) - x + 1 +--R +--R Type: Expression Integer +--E 56 + +--S 57 of 127 +solve(ode221,y,x) +--R +--R +--R (57) "failed" +--R Type: Union("failed",...) +--E 57 + +--S 58 of 127 +ode222 := (2*y(x)+x+7)*D(y(x),x)-y(x)+2*x+4 +--R +--R +--R , +--R (58) (2y(x) + x + 7)y (x) - y(x) + 2x + 4 +--R +--R Type: Expression Integer +--E 58 + +--S 59 of 127 +solve(ode222,y,x) +--R +--R +--R (59) "failed" +--R Type: Union("failed",...) +--E 59 + +--S 60 of 127 +ode223 := (2*y(x)-x)*D(y(x),x)-y(x)-2*x +--R +--R +--R , +--R (60) (2y(x) - x)y (x) - y(x) - 2x +--R +--R Type: Expression Integer +--E 60 + +--S 61 of 127 +yx:=solve(ode223,y,x) +--R +--R +--R 2 2 +--R (61) y(x) - x y(x) - x +--R Type: Union(Expression Integer,...) +--E 61 + +--S 62 of 127 +ode223expr := (2*yx-x)*D(yx,x)-yx-2*x +--R +--R +--R (62) +--R 3 2 2 3 2 , 3 +--R (4y(x) - 6x y(x) + (- 2x - 2x)y(x) + 2x + x )y (x) - 2y(x) +--R +--R + +--R 2 2 3 2 +--R (- 2x - 1)y(x) + (6x + 2x)y(x) + 4x + 3x - 2x +--R Type: Expression Integer +--E 62 + +--S 63 of 127 +ode224 := (2*y(x)-6*x)*D(y(x),x)-y(x)+3*x+2 +--R +--R +--R , +--R (63) (2y(x) - 6x)y (x) - y(x) + 3x + 2 +--R +--R Type: Expression Integer +--E 63 + +--S 64 of 127 +solve(ode224,y,x) +--R +--R +--R (64) "failed" +--R Type: Union("failed",...) +--E 64 + +--S 65 of 127 +ode225 := (4*y(x)+2*x+3)*D(y(x),x)-2*y(x)-x-1 +--R +--R +--R , +--R (65) (4y(x) + 2x + 3)y (x) - 2y(x) - x - 1 +--R +--R Type: Expression Integer +--E 65 + +--S 66 of 127 +solve(ode225,y,x) +--R +--R +--R (66) "failed" +--R Type: Union("failed",...) +--E 66 + +--S 67 of 127 +ode226 := (4*y(x)-2*x-3)*D(y(x),x)+2*y(x)-x-1 +--R +--R +--R , +--R (67) (4y(x) - 2x - 3)y (x) + 2y(x) - x - 1 +--R +--R Type: Expression Integer +--E 67 + +--S 68 of 127 +solve(ode226,y,x) +--R +--R +--R (68) "failed" +--R Type: Union("failed",...) +--E 68 + +--S 69 of 127 +ode227 := (4*y(x)-3*x-5)*D(y(x),x)-3*y(x)+7*x+2 +--R +--R +--R , +--R (69) (4y(x) - 3x - 5)y (x) - 3y(x) + 7x + 2 +--R +--R Type: Expression Integer +--E 69 + +--S 70 of 127 +yx:=solve(ode227,y,x) +--R +--R +--R 2 2 +--R 4y(x) + (- 6x - 10)y(x) + 7x + 4x +--R (70) ----------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 70 + +--S 71 of 127 +ode227expr := (4*yx-3*x-5)*D(yx,x)-3*yx+7*x+2 +--R +--R +--R (71) +--R 3 2 2 3 +--R 64y(x) + (- 144x - 240)y(x) + (184x + 280x + 160)y(x) - 84x +--R + +--R 2 +--R - 170x - 20x + 50 +--R * +--R , +--R y (x) +--R +--R + +--R 3 2 2 3 2 +--R - 48y(x) + (184x + 140)y(x) + (- 252x - 340x - 20)y(x) + 196x + 105x +--R + +--R - 48x - 16 +--R / +--R 2 +--R Type: Expression Integer +--E 71 + +--S 72 of 127 +ode228 := (4*y(x)+11*x-11) *D(y(x),x)-25*y(x)-8*x+62 +--R +--R +--R , +--R (72) (4y(x) + 11x - 11)y (x) - 25y(x) - 8x + 62 +--R +--R Type: Expression Integer +--E 72 + +--S 73 of 127 +solve(ode228,y,x) +--R +--R +--R (73) "failed" +--R Type: Union("failed",...) +--E 73 + +--S 74 of 127 +ode229 := (12*y(x)-5*x-8)*D(y(x),x)-5*y(x)+2*x+3 +--R +--R +--R , +--R (74) (12y(x) - 5x - 8)y (x) - 5y(x) + 2x + 3 +--R +--R Type: Expression Integer +--E 74 + +--S 75 of 127 +yx:=solve(ode229,y,x) +--R +--R +--R 2 2 +--R (75) 6y(x) + (- 5x - 8)y(x) + x + 3x +--R Type: Union(Expression Integer,...) +--E 75 + +--S 76 of 127 +ode229expr := (12*yx-5*x-8)*D(yx,x)-5*yx+2*x+3 +--R +--R +--R (76) +--R 3 2 2 3 +--R 864y(x) + (- 1080x - 1728)y(x) + (444x + 1332x + 672)y(x) - 60x +--R + +--R 2 +--R - 251x - 208x + 64 +--R * +--R , +--R y (x) +--R +--R + +--R 3 2 2 3 2 +--R - 360y(x) + (444x + 666)y(x) + (- 180x - 502x - 208)y(x) + 24x + 93x +--R + +--R 64x - 21 +--R Type: Expression Integer +--E 76 + +--S 77 of 127 +ode230 := a*y(x)*D(y(x),x)+b*y(x)**2+f(x) +--R +--R +--R , 2 +--R (77) a y(x)y (x) + b y(x) + f(x) +--R +--R Type: Expression Integer +--E 77 + +--S 78 of 127 +solve(ode230,y,x) +--R +--R +--I 2%I b +--R x ----- +--R ++ 2 a +--I (78) | (b y(x) + f(%I))%e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 of 127 +ode231 := (a*y(x)+b*x+c)*D(y(x),x)+alpha*y(x)+beta*x+gamma +--R +--R +--R , +--R (79) (a y(x) + b x + c)y (x) + alpha y(x) + beta x + gamma +--R +--R Type: Expression Integer +--E 79 + +--S 80 of 127 +solve(ode231,y,x) +--R +--R +--R (80) "failed" +--R Type: Union("failed",...) +--E 80 + +--S 81 of 127 +ode232 := x*y(x)*D(y(x),x)+y(x)**2+x**2 +--R +--R +--R , 2 2 +--R (81) x y(x)y (x) + y(x) + x +--R +--R Type: Expression Integer +--E 81 + +--S 82 of 127 +yx:=solve(ode232,y,x) +--R +--R +--R 2 2 4 +--R 2x y(x) + x +--R (82) ------------- +--R 4 +--R Type: Union(Expression Integer,...) +--E 82 + +--S 83 of 127 +ode232expr := x*yx*D(yx,x)+yx**2+x**2 +--R +--R +--R 5 3 7 , 4 4 6 2 8 2 +--R (8x y(x) + 4x y(x))y (x) + 12x y(x) + 16x y(x) + 5x + 16x +--R +--R (83) -------------------------------------------------------------- +--R 16 +--R Type: Expression Integer +--E 83 + +--S 84 of 127 +ode233 := x*y(x)*D(y(x),x)-y(x)**2+a*x**3*cos(x) +--R +--R +--R , 3 2 +--R (84) x y(x)y (x) + a x cos(x) - y(x) +--R +--R Type: Expression Integer +--E 84 + +--S 85 of 127 +yx:=solve(ode233,y,x) +--R +--R +--R 2 2 +--R 2a x sin(x) + y(x) +--R (85) ------------------- +--R 2 +--R 2x +--R Type: Union(Expression Integer,...) +--E 85 + +--S 86 of 127 +ode233expr := x*yx*D(yx,x)-yx**2+a*x**3*cos(x) +--R +--R +--R (86) +--R 3 3 , 2 4 2 +--R (4a x y(x)sin(x) + 2x y(x) )y (x) - 4a x sin(x) +--R +--R + +--R 2 5 2 2 3 2 7 4 +--R (4a x cos(x) - 8a x y(x) )sin(x) + (2a x y(x) + 4a x )cos(x) - 3y(x) +--R / +--R 4 +--R 4x +--R Type: Expression Integer +--E 86 + +--S 87 of 127 +ode234 := x*y(x)*D(y(x),x)-y(x)**2+x*y(x)+x**3-2*x**2 +--R +--R +--R , 2 3 2 +--R (87) x y(x)y (x) - y(x) + x y(x) + x - 2x +--R +--R Type: Expression Integer +--E 87 + +--S 88 of 127 +solve(ode234,y,x) +--R +--R +--R (88) "failed" +--R Type: Union("failed",...) +--E 88 + +--S 89 of 127 +ode235 := (x*y(x)+a)*D(y(x),x)+b*y(x) +--R +--R +--R , +--R (89) (x y(x) + a)y (x) + b y(x) +--R +--R Type: Expression Integer +--E 89 + +--S 90 of 127 +yx:=solve(ode235,y,x) +--R +--R +--R y(x) +--R ---- +--R b y(x) +--R (90) b x %e + a Ei(----) +--R b +--R Type: Union(Expression Integer,...) +--E 90 + +--S 91 of 127 +ode235expr := (x*yx+a)*D(yx,x)+b*yx +--R +--R +--R (91) +--R y(x) 2 +--R ---- +--R 3 2 b +--R (b x y(x) + a b x )(%e ) +--R + +--R y(x) +--R ---- +--R 2 2 y(x) 2 b +--R ((a x y(x) + a x)Ei(----) + a x y(x) + a )%e +--R b +--R * +--R , +--R y (x) +--R +--R + +--R y(x) 2 y(x) +--R ---- ---- +--R 2 2 b y(x) 2 b +--R b x y(x)(%e ) + (a b x y(x)Ei(----) + (b x + a b)y(x))%e +--R b +--R + +--R y(x) +--R a b y(x)Ei(----) +--R b +--R / +--R y(x) +--R Type: Expression Integer +--E 91 + +--S 92 of 127 +ode236 := x*(y(x)+4)*D(y(x),x)-y(x)**2-2*y(x)-2*x +--R +--R +--R , 2 +--R (92) (x y(x) + 4x)y (x) - y(x) - 2y(x) - 2x +--R +--R Type: Expression Integer +--E 92 + +--S 93 of 127 +solve(ode236,y,x) +--R +--R +--R (93) "failed" +--R Type: Union("failed",...) +--E 93 + +--S 94 of 127 +ode237 := x*(y(x)+a)*D(y(x),x)+b*y(x)+c*x +--R +--R +--R , +--R (94) (x y(x) + a x)y (x) + b y(x) + c x +--R +--R Type: Expression Integer +--E 94 + +--S 95 of 127 +solve(ode237,y,x) +--R +--R +--R (95) "failed" +--R Type: Union("failed",...) +--E 95 + +--S 96 of 127 +ode238 := (x*(y(x)+x)+a)*D(y(x),x)-y(x)*(y(x)+x)-b +--R +--R +--R 2 , 2 +--R (96) (x y(x) + x + a)y (x) - y(x) - x y(x) - b +--R +--R Type: Expression Integer +--E 96 + +--S 97 of 127 +solve(ode238,y,x) +--R +--R +--R (97) "failed" +--R Type: Union("failed",...) +--E 97 + +--S 98 of 127 +ode239 := (x*y(x)-x**2)*D(y(x),x)+y(x)**2-3*x*y(x)-2*x**2 +--R +--R +--R 2 , 2 2 +--R (98) (x y(x) - x )y (x) + y(x) - 3x y(x) - 2x +--R +--R Type: Expression Integer +--E 98 + +--S 99 of 127 +yx:=solve(ode239,y,x) +--R +--R +--R 2 2 3 4 +--R x y(x) - 2x y(x) - x +--R (99) ---------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 99 + +--S 100 of 127 +ode239expr := (x*yx-x**2)*D(yx,x)+yx**2-3*x*yx-2*x**2 +--R +--R +--R (100) +--R 5 3 6 2 7 4 8 5 , 4 4 +--R (2x y(x) - 6x y(x) + (2x - 4x )y(x) + 2x + 4x )y (x) + 3x y(x) +--R +--R + +--R 5 3 6 3 2 7 4 8 5 2 +--R - 14x y(x) + (8x - 10x )y(x) + (18x + 24x )y(x) + 5x + 14x - 8x +--R / +--R 4 +--R Type: Expression Integer +--E 100 + +--S 101 of 127 +ode240 := 2*x*y(x)*D(y(x),x)-y(x)**2+a*x +--R +--R +--R , 2 +--R (101) 2x y(x)y (x) - y(x) + a x +--R +--R Type: Expression Integer +--E 101 + +--S 102 of 127 +yx:=solve(ode240,y,x) +--R +--R +--R 2 +--R a x log(x) + y(x) +--R (102) ------------------ +--R x +--R Type: Union(Expression Integer,...) +--E 102 + +--S 103 of 127 +ode240expr := 2*x*yx*D(yx,x)-yx**2+a*x +--R +--R +--R (103) +--R 2 3 , 2 2 2 +--R (4a x y(x)log(x) + 4x y(x) )y (x) - a x log(x) +--R +--R + +--R 2 2 2 4 2 3 +--R (- 4a x y(x) + 2a x )log(x) - 3y(x) + 2a x y(x) + a x +--R / +--R 2 +--R x +--R Type: Expression Integer +--E 103 + +--S 104 of 127 +ode241 := 2*x*y(x)*D(y(x),x)-y(x)**2+a*x**2 +--R +--R +--R , 2 2 +--R (104) 2x y(x)y (x) - y(x) + a x +--R +--R Type: Expression Integer +--E 104 + +--S 105 of 127 +yx:=solve(ode241,y,x) +--R +--R +--R 2 2 +--R y(x) + a x +--R (105) ------------ +--R x +--R Type: Union(Expression Integer,...) +--E 105 + +--S 106 of 127 +ode241expr := 2*x*yx*D(yx,x)-yx**2+a*x**2 +--R +--R +--R 3 3 , 4 2 2 2 4 +--R (4x y(x) + 4a x y(x))y (x) - 3y(x) - 2a x y(x) + (a + a)x +--R +--R (106) -------------------------------------------------------------- +--R 2 +--R x +--R Type: Expression Integer +--E 106 + +--S 107 of 127 +ode242 := 2*x*y(x)*D(y(x),x)+2*y(x)**2+1 +--R +--R +--R , 2 +--R (107) 2x y(x)y (x) + 2y(x) + 1 +--R +--R Type: Expression Integer +--E 107 + +--S 108 of 127 +yx:=solve(ode242,y,x) +--R +--R +--R 2 2 2 +--R 2x y(x) + x +--R (108) ------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 108 + +--S 109 of 127 +ode242expr := 2*x*yx*D(yx,x)+2*yx**2+1 +--R +--R +--R 5 3 5 , 4 4 4 2 4 +--R (8x y(x) + 4x y(x))y (x) + 12x y(x) + 12x y(x) + 3x + 2 +--R +--R (109) ----------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 109 + +--S 110 of 127 +ode243 := x*(2*y(x)+x-1)*D(y(x),x)-y(x)*(y(x)+2*x+1) +--R +--R +--R 2 , 2 +--R (110) (2x y(x) + x - x)y (x) - y(x) + (- 2x - 1)y(x) +--R +--R Type: Expression Integer +--E 110 + +--S 111 of 127 +solve(ode243,y,x) +--R +--R +--R (111) "failed" +--R Type: Union("failed",...) +--E 111 + +--S 112 of 127 +ode244 := x*(2*y(x)-x-1)*D(y(x),x)+y(x)*(2*x-y(x)-1) +--R +--R +--R 2 , 2 +--R (112) (2x y(x) - x - x)y (x) - y(x) + (2x - 1)y(x) +--R +--R Type: Expression Integer +--E 112 + +--S 113 of 127 +solve(ode244,y,x) +--R +--R +--R (113) "failed" +--R Type: Union("failed",...) +--E 113 + +--S 114 of 127 +ode245 := (2*x*y(x)+4*x**3)*D(y(x),x)+y(x)**2+112*x**2*y(x) +--R +--R +--R 3 , 2 2 +--R (114) (2x y(x) + 4x )y (x) + y(x) + 112x y(x) +--R +--R Type: Expression Integer +--E 114 + +--S 115 of 127 +solve(ode245,y,x) +--R +--R +--R (115) "failed" +--R Type: Union("failed",...) +--E 115 + +--S 116 of 127 +ode246 := x*(3*y(x)+2*x)*D(y(x),x)+3*(y(x)+x)**2 +--R +--R +--R 2 , 2 2 +--R (116) (3x y(x) + 2x )y (x) + 3y(x) + 6x y(x) + 3x +--R +--R Type: Expression Integer +--E 116 + +--S 117 of 127 +yx:=solve(ode246,y,x) +--R +--R +--R 2 2 3 4 +--R 6x y(x) + 8x y(x) + 3x +--R (117) ------------------------ +--R 4 +--R Type: Union(Expression Integer,...) +--E 117 + +--S 118 of 127 +ode246expr := x*(3*yx+2*x)*D(yx,x)+3*(yx+x)**2 +--R +--R +--R (118) +--R 5 3 6 2 7 4 8 5 , +--R (216x y(x) + 432x y(x) + (300x + 96x )y(x) + 72x + 64x )y (x) +--R +--R + +--R 4 4 5 3 6 3 2 7 4 +--R 324x y(x) + 1008x y(x) + (1200x + 240x )y(x) + (648x + 384x )y(x) +--R + +--R 8 5 2 +--R 135x + 168x + 48x +--R / +--R 16 +--R Type: Expression Integer +--E 118 + +--S 119 of 127 +ode247 := (3*x+2)*(y(x)-2*x-1)*D(y(x),x)-y(x)**2+x*y(x)-7*x**2-9*x-3 +--R +--R +--R 2 , 2 2 +--R (119) ((3x + 2)y(x) - 6x - 7x - 2)y (x) - y(x) + x y(x) - 7x - 9x - 3 +--R +--R Type: Expression Integer +--E 119 + +--S 120 of 127 +solve(ode247,y,x) +--R +--R +--R (120) "failed" +--R Type: Union("failed",...) +--E 120 + +--S 121 of 127 +ode248 := (6*x*y(x)+x**2+3)*D(y(x),x)+3*y(x)**2+2*x*y(x)+2*x +--R +--R +--R 2 , 2 +--R (121) (6x y(x) + x + 3)y (x) + 3y(x) + 2x y(x) + 2x +--R +--R Type: Expression Integer +--E 121 + +--S 122 of 127 +yx:=solve(ode248,y,x) +--R +--R +--R 2 2 2 +--R (122) 3x y(x) + (x + 3)y(x) + x +--R Type: Union(Expression Integer,...) +--E 122 + +--S 123 of 127 +ode248expr := (6*x*yx+x**2+3)*D(yx,x)+3*yx**2+2*x*yx+2*x +--R +--R +--R (123) +--R 3 3 4 2 2 5 4 3 5 +--R 108x y(x) + (54x + 162x )y(x) + (6x + 36x + 42x + 72x)y(x) + 6x +--R + +--R 4 3 2 +--R x + 18x + 6x + 9 +--R * +--R , +--R y (x) +--R +--R + +--R 2 4 3 3 4 3 2 2 +--R 81x y(x) + (72x + 108x)y(x) + (15x + 72x + 63x + 36)y(x) +--R + +--R 4 3 2 4 3 +--R (30x + 4x + 54x + 12x)y(x) + 15x + 4x + 8x +--R Type: Expression Integer +--E 123 + +--S 124 of 127 +ode249 := (a*x*y(x)+b*x**n)*D(y(x),x)+alpha*y(x)**3+beta*y(x)**2 +--R +--R +--R n , 3 2 +--R (124) (b x + a x y(x))y (x) + alpha y(x) + beta y(x) +--R +--R Type: Expression Integer +--E 124 + +--S 125 of 127 +solve(ode249,y,x) +--R +--R +--R (125) "failed" +--R Type: Union("failed",...) +--E 125 + +--S 126 of 127 +ode250 := (B*x*y(x)+A*x**2+a*x+b*y(x)+c)*D(y(x),x)-B*g(x)**2+_ + A*x*y(x)+alpha*x+beta*y(x)+gamma +--R +--R +--R (126) +--R 2 , 2 +--R ((B x + b)y(x) + A x + a x + c)y (x) + (A x + beta)y(x) - B g(x) +--R +--R + +--R alpha x + gamma +--R Type: Expression Integer +--E 126 + +--S 127 of 127 +solve(ode250,y,x) +--R +--R +--R (127) "failed" +--R Type: Union("failed",...) +--E 127 + +)spool +)lisp (bye) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} {\bf http://www.cs.uwaterloo.ca/$\tilde{}$ecterrab/odetools.html} +\end{thebibliography} +\end{document} + diff --git a/src/axiom-website/CATS/kamke4.input.pdf b/src/axiom-website/CATS/kamke4.input.pdf new file mode 100644 index 0000000..ac75173 --- /dev/null +++ b/src/axiom-website/CATS/kamke4.input.pdf @@ -0,0 +1,2203 @@ +%PDF-1.2 +7 0 obj +<< +/Type/Encoding 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+\maketitle +\begin{abstract} +This is the 251-300 of the Kamke test suite as published by +E. S. Cheb-Terrab\cite{1}. They have been rewritten using Axiom +syntax. Where possible we show that the particular solution actually +satisfies the original ordinary differential equation. +\end{abstract} +\eject +\tableofcontents +\eject +<<*>>= +)spool kamke5.output +)set break resume +)set mes auto off +)clear all + +--S 1 of 130 +y:=operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 1 + +--S 2 of 130 +f:=operator 'f +--R +--R +--R (2) f +--R Type: BasicOperator +--E 2 + +--S 3 of 130 +f0:=operator 'f0 +--R +--R +--R (3) f0 +--R Type: BasicOperator +--E 3 + +--S 4 of 130 +f1:=operator 'f1 +--R +--R +--R (4) f1 +--R Type: BasicOperator +--E 4 + +--S 5 of 130 +f2:=operator 'f2 +--R +--R +--R (5) f2 +--R Type: BasicOperator +--E 5 + +--S 6 of 130 +f3:=operator 'f3 +--R +--R +--R (6) f3 +--R Type: BasicOperator +--E 6 + +--S 7 of 130 +g:=operator 'g +--R +--R +--R (7) g +--R Type: BasicOperator +--E 7 + +--S 8 of 130 +g0:=operator 'g0 +--R +--R +--R (8) g0 +--R Type: BasicOperator +--E 8 + +--S 9 of 130 +g1:=operator 'g1 +--R +--R +--R (9) g1 +--R Type: BasicOperator +--E 9 + +--S 10 of 130 +h:=operator 'h +--R +--R +--R (10) h +--R Type: BasicOperator +--E 10 + +--S 11 of 130 +ode251 := (x**2*y(x)-1)*D(y(x),x)+x*y(x)**2-1 +--R +--R +--R 2 , 2 +--R (11) (x y(x) - 1)y (x) + x y(x) - 1 +--R +--R Type: Expression Integer +--E 11 + +--S 12 of 130 +yx:=solve(ode251,y,x) +--R +--R +--R 2 2 +--R x y(x) - 2y(x) - 2x +--R (12) -------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 12 + +--S 13 of 130 +ode251expr := (x**2*yx-1)*D(yx,x)+x*yx**2-1 +--R +--R +--R (13) +--R 6 3 4 2 5 3 , 5 4 3 3 +--R (2x y(x) - 6x y(x) - 4x y(x) + 4x + 4)y (x) + 3x y(x) - 8x y(x) +--R +--R + +--R 4 2 2 3 +--R - 10x y(x) + 12x y(x) + 8x +--R / +--R 4 +--R Type: Expression Integer +--E 13 + +--S 14 of 130 +ode252 := (x**2*y(x)-1)*D(y(x),x)-(x*y(x)**2-1) +--R +--R +--R 2 , 2 +--R (14) (x y(x) - 1)y (x) - x y(x) + 1 +--R +--R Type: Expression Integer +--E 14 + +--S 15 of 130 +solve(ode252,y,x) +--R +--R +--R (15) "failed" +--R Type: Union("failed",...) +--E 15 + +--S 16 of 130 +ode253 := (x**2*y(x)-1)*D(y(x),x)+8*(x*y(x)**2-1) +--R +--R +--R 2 , 2 +--R (16) (x y(x) - 1)y (x) + 8x y(x) - 8 +--R +--R Type: Expression Integer +--E 16 + +--S 17 of 130 +solve(ode253,y,x) +--R +--R +--R (17) "failed" +--R Type: Union("failed",...) +--E 17 + +--S 18 of 130 +ode254 := x*(x*y(x)-2)*D(y(x),x)+x**2*y(x)**3+x*y(x)**2-2*y(x) +--R +--R +--R 2 , 2 3 2 +--R (18) (x y(x) - 2x)y (x) + x y(x) + x y(x) - 2y(x) +--R +--R Type: Expression Integer +--E 18 + +--S 19 of 130 +solve(ode254,y,x) +--R +--R +--R (19) "failed" +--R Type: Union("failed",...) +--E 19 + +--S 20 of 130 +ode255 := x*(x*y(x)-3)*D(y(x),x)+x*y(x)**2-y(x) +--R +--R +--R 2 , 2 +--R (20) (x y(x) - 3x)y (x) + x y(x) - y(x) +--R +--R Type: Expression Integer +--E 20 + +--S 21 of 130 +solve(ode255,y,x) +--R +--R +--R (21) "failed" +--R Type: Union("failed",...) +--E 21 + +--S 22 of 130 +ode256 := x**2*(y(x)-1)*D(y(x),x)+(x-1)*y(x) +--R +--R +--R 2 2 , +--R (22) (x y(x) - x )y (x) + (x - 1)y(x) +--R +--R Type: Expression Integer +--E 22 + +--S 23 of 130 +solve(ode256,y,x) +--R +--R +--R (23) "failed" +--R Type: Union("failed",...) +--E 23 + +--S 24 of 130 +ode257 := x*(x*y(x)+x**4-1)*D(y(x),x)-y(x)*(x*y(x)-x**4-1) +--R +--R +--R 2 5 , 2 4 +--R (24) (x y(x) + x - x)y (x) - x y(x) + (x + 1)y(x) +--R +--R Type: Expression Integer +--E 24 + +--S 25 of 130 +solve(ode257,y,x) +--R +--R +--R (25) "failed" +--R Type: Union("failed",...) +--E 25 + +--S 26 of 130 +ode258 := 2*x**2*y(x)*D(y(x),x)+y(x)**2-2*x**3-x**2 +--R +--R +--R 2 , 2 3 2 +--R (26) 2x y(x)y (x) + y(x) - 2x - x +--R +--R Type: Expression Integer +--E 26 + +--S 27 of 130 +yx:=solve(ode258,y,x) +--R +--R +--R 1 +--R - - +--R 2 2 x +--R (27) (y(x) - x )%e +--R Type: Union(Expression Integer,...) +--E 27 + +--S 28 of 130 +ode258expr := 2*x**2*yx*D(yx,x)+yx**2-2*x**3-x**2 +--R +--R +--R (28) +--R 1 2 +--R - - +--R 2 3 4 x , +--R (4x y(x) - 4x y(x))(%e ) y (x) +--R +--R + +--R 1 2 +--R - - +--R 4 3 2 2 5 4 x 3 2 +--R (3y(x) + (- 4x - 6x )y(x) + 4x + 3x )(%e ) - 2x - x +--R Type: Expression Integer +--E 28 + +--S 29 of 130 +ode259 := 2*x**2*y(x)*D(y(x),x)-y(x)**2-x**2*exp(x-1/x) +--R +--R +--R 2 +--R x - 1 +--R ------ +--R 2 , 2 x 2 +--R (29) 2x y(x)y (x) - x %e - y(x) +--R +--R Type: Expression Integer +--E 29 + +--S 30 of 130 +yx:=solve(ode259,y,x) +--R +--R +--R 2 +--R 1 x - 1 1 +--R - ------ - +--R x x 2 x +--R (30) - %e %e + y(x) %e +--R Type: Union(Expression Integer,...) +--E 30 + +--S 31 of 130 +ode259expr := 2*x**2*yx*D(yx,x)-yx**2-x**2*exp(x-1/x) +--R +--R +--R (31) +--R 2 +--R 1 2 x - 1 1 2 +--R - ------ - +--R 2 x x 2 3 x , +--R (- 4x y(x)(%e ) %e + 4x y(x) (%e ) )y (x) +--R +--R + +--R 2 2 2 +--R 1 2 x - 1 1 2 x - 1 +--R - ------ - ------ +--R 2 x x 2 2 x 2 x +--R (2x - 1)(%e ) (%e ) + ((- 2x + 4)y(x) (%e ) - x )%e +--R + +--R 1 2 +--R - +--R 4 x +--R - 3y(x) (%e ) +--R Type: Expression Integer +--E 31 + +--S 32 of 130 +ode260 := (2*x**2*y(x)+x)*D(y(x),x)-x**2*y(x)**3+2*x*y(x)**2+y(x) +--R +--R +--R 2 , 2 3 2 +--R (32) (2x y(x) + x)y (x) - x y(x) + 2x y(x) + y(x) +--R +--R Type: Expression Integer +--E 32 + +--S 33 of 130 +solve(ode260,y,x) +--R +--R +--R (33) "failed" +--R Type: Union("failed",...) +--E 33 + +--S 34 of 130 +ode261 := (2*x**2*y(x)-x)*D(y(x),x)-2*x*y(x)**2-y(x) +--R +--R +--R 2 , 2 +--R (34) (2x y(x) - x)y (x) - 2x y(x) - y(x) +--R +--R Type: Expression Integer +--E 34 + +--S 35 of 130 +solve(ode261,y,x) +--R +--R +--R (35) "failed" +--R Type: Union("failed",...) +--E 35 + +--S 36 of 130 +ode262 := (2*x**2*y(x)-x**3)*D(y(x),x)+y(x)**3-4*x*y(x)**2+2*x**3 +--R +--R +--R 2 3 , 3 2 3 +--R (36) (2x y(x) - x )y (x) + y(x) - 4x y(x) + 2x +--R +--R Type: Expression Integer +--E 36 + +--S 37 of 130 +solve(ode262,y,x) +--R +--R +--R (37) "failed" +--R Type: Union("failed",...) +--E 37 + +--S 38 of 130 +ode263 := 2*x**3+y(x)*D(y(x),x)+3*x**2*y(x)**2+7 +--R +--R +--R , 2 2 3 +--R (38) y(x)y (x) + 3x y(x) + 2x + 7 +--R +--R Type: Expression Integer +--E 38 + +--S 39 of 130 +solve(ode263,y,x) +--R +--R +--R x 3 +--I ++ 2 2 3 2%K +--I (39) | (3%K y(x) + 2%K + 7)%e d%K +--R ++ +--R Type: Union(Expression Integer,...) +--E 39 + +--S 40 of 130 +ode264 := 2*x*(x**3*y(x)+1)*D(y(x),x)+(3*x**3*y(x)-1)*y(x) +--R +--R +--R 4 , 3 2 +--R (40) (2x y(x) + 2x)y (x) + 3x y(x) - y(x) +--R +--R Type: Expression Integer +--E 40 + +--S 41 of 130 +solve(ode264,y,x) +--R +--R +--R (41) "failed" +--R Type: Union("failed",...) +--E 41 + +--S 42 of 130 +ode265 := (x**(n*(n+1))*y(x)-1)*D(y(x),x)+2*(n+1)**2*x**(n-1)_ + *(x**(n**2)*y(x)**2-1) +--R +--R +--R (42) +--R 2 2 +--R n + n , 2 2 n - 1 n +--R (y(x)x - 1)y (x) + (2n + 4n + 2)y(x) x x +--R +--R + +--R 2 n - 1 +--R (- 2n - 4n - 2)x +--R Type: Expression Integer +--E 42 + +--S 43 of 130 +solve(ode265,y,x) +--R +--R +--R (43) "failed" +--R Type: Union("failed",...) +--E 43 + +--S 44 of 130 +ode266 := (y(x)-x)*sqrt(x**2+1)*D(y(x),x)-a*sqrt((y(x)**2+1)**3) +--R +--R +--R +------+ +---------------------------+ +--R | 2 , | 6 4 2 +--R (44) (y(x) - x)\|x + 1 y (x) - a\|y(x) + 3y(x) + 3y(x) + 1 +--R +--R Type: Expression Integer +--E 44 + +--S 45 of 130 +solve(ode266,y,x) +--R +--R +--R (45) "failed" +--R Type: Union("failed",...) +--E 45 + +--S 46 of 130 +ode267 := y(x)*D(y(x),x)*sin(x)**2+y(x)**2*cos(x)*sin(x)-1 +--R +--R +--R 2 , 2 +--R (46) y(x)sin(x) y (x) + y(x) cos(x)sin(x) - 1 +--R +--R Type: Expression Integer +--E 46 + +--S 47 of 130 +yx:=solve(ode267,y,x) +--R +--R +--R 2 2 +--R y(x) sin(x) - 2x +--R (47) ----------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 47 + +--S 48 of 130 +ode267expr := yx*D(yx,x)*sin(x)**2+yx**2*cos(x)*sin(x)-1 +--R +--R +--R (48) +--R 3 6 4 , 4 5 +--R (2y(x) sin(x) - 4x y(x)sin(x) )y (x) + 3y(x) cos(x)sin(x) +--R +--R + +--R 2 4 2 3 2 2 +--R - 2y(x) sin(x) - 8x y(x) cos(x)sin(x) + 4x sin(x) + 4x cos(x)sin(x) - 4 +--R / +--R 4 +--R Type: Expression Integer +--E 48 + +--S 49 of 130 +ode268 := f(x)*y(x)*D(y(x),x)+g(x)*y(x)**2+h(x) +--R +--R +--R , 2 +--R (49) f(x)y(x)y (x) + g(x)y(x) + h(x) +--R +--R Type: Expression Integer +--E 49 + +--S 50 of 130 +solve(ode268,y,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 50 + +--S 51 of 130 +ode269 := (g1(x)*y(x)+g0(x))*D(y(x),x)-f1(x)*y(x)-_ + f2(x)*y(x)**2-f3(x)*y(x)**3-f0(x) +--R +--R +--R (50) +--R , 3 2 +--R (g1(x)y(x) + g0(x))y (x) - f3(x)y(x) - f2(x)y(x) - f1(x)y(x) - f0(x) +--R +--R Type: Expression Integer +--E 51 + +--S 52 of 130 +solve(ode269,y,x) +--R +--R +--R (51) "failed" +--R Type: Union("failed",...) +--E 52 + +--S 53 of 130 +ode270 := (y(x)**2-x)*D(y(x),x)-y(x)+x**2 +--R +--R +--R 2 , 2 +--R (52) (y(x) - x)y (x) - y(x) + x +--R +--R Type: Expression Integer +--E 53 + +--S 54 of 130 +yx:=solve(ode270,y,x) +--R +--R +--R 3 3 +--R y(x) - 3x y(x) + x +--R (53) -------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 54 + +--S 55 of 130 +ode270expr := (yx**2-x)*D(yx,x)-yx+x**2 +--R +--R +--R (54) +--R 8 6 3 5 2 4 4 3 +--R y(x) - 7x y(x) + 2x y(x) + 15x y(x) - 8x y(x) +--R + +--R 6 3 2 5 7 2 +--R (x - 9x - 9x)y(x) + 6x y(x) - x + 9x +--R * +--R , +--R y (x) +--R +--R + +--R 7 2 6 5 3 4 5 2 3 +--R - y(x) + x y(x) + 6x y(x) - 8x y(x) + (2x - 9x - 3)y(x) +--R + +--R 4 2 6 8 3 2 +--R 15x y(x) + (- 7x + 18x)y(x) + x - 12x + 9x +--R / +--R 9 +--R Type: Expression Integer +--E 55 + +--S 56 of 130 +ode271 := (y(x)**2+x**2)*D(y(x),x)+2*x*(y(x)+2*x) +--R +--R +--R 2 2 , 2 +--R (55) (y(x) + x )y (x) + 2x y(x) + 4x +--R +--R Type: Expression Integer +--E 56 + +--S 57 of 130 +yx:=solve(ode271,y,x) +--R +--R +--R 3 2 3 +--R y(x) + 3x y(x) + 4x +--R (56) --------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 57 + +--S 58 of 130 +ode271expr := (yx**2+x**2)*D(yx,x)+2*x*(yx+2*x) +--R +--R +--R (57) +--R 8 2 6 3 5 4 4 5 3 +--R y(x) + 7x y(x) + 8x y(x) + 15x y(x) + 32x y(x) +--R + +--R 6 2 2 7 8 4 +--R (25x + 9x )y(x) + 24x y(x) + 16x + 9x +--R * +--R , +--R y (x) +--R +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 2x y(x) + 4x y(x) + 12x y(x) + 40x y(x) + (50x + 6x)y(x) +--R + +--R 6 2 7 3 8 4 2 +--R 84x y(x) + (128x + 36x )y(x) + 64x + 60x + 36x +--R / +--R 9 +--R Type: Expression Integer +--E 58 + +--S 59 of 130 +ode272 := (y(x)**2+x**2)*D(y(x),x)-y(x)**2 +--R +--R +--R 2 2 , 2 +--R (58) (y(x) + x )y (x) - y(x) +--R +--R Type: Expression Integer +--E 59 + +--S 60 of 130 +solve(ode272,y,x) +--R +--R +--R (59) "failed" +--R Type: Union("failed",...) +--E 60 + +--S 61 of 130 +ode273 := (y(x)**2+x**2+a)*D(y(x),x)+2*x*y(x) +--R +--R +--R 2 2 , +--R (60) (y(x) + x + a)y (x) + 2x y(x) +--R +--R Type: Expression Integer +--E 61 + +--S 62 of 130 +yx:=solve(ode273,y,x) +--R +--R +--R 3 2 +--R y(x) + (3x + 3a)y(x) +--R (61) ---------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 62 + +--S 63 of 130 +ode273expr := (yx**2+x**2+a)*D(yx,x)+2*x*yx +--R +--R +--R (62) +--R 8 2 6 4 2 2 4 +--R y(x) + (7x + 7a)y(x) + (15x + 30a x + 15a )y(x) +--R + +--R 6 4 2 2 3 2 4 2 2 +--R (9x + 27a x + (27a + 9)x + 9a + 9a)y(x) + 9x + 18a x + 9a +--R * +--R , +--R y (x) +--R +--R + +--R 7 3 5 5 3 2 3 +--R 2x y(x) + (12x + 12a x)y(x) + (18x + 36a x + (18a + 6)x)y(x) +--R + +--R 3 +--R (36x + 36a x)y(x) +--R / +--R 9 +--R Type: Expression Integer +--E 63 + +--S 64 of 130 +ode274 := (y(x)**2+x**2+a)*D(y(x),x)+2*x*y(x)+x**2+b +--R +--R +--R 2 2 , 2 +--R (63) (y(x) + x + a)y (x) + 2x y(x) + x + b +--R +--R Type: Expression Integer +--E 64 + +--S 65 of 130 +yx:=solve(ode274,y,x) +--R +--R +--R 3 2 3 +--R y(x) + (3x + 3a)y(x) + x + 3b x +--R (64) ---------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 65 + +--S 66 of 130 +ode274expr := (yx**2+x**2+a)*D(yx,x)+2*x*yx+x**2+b +--R +--R +--R (65) +--R 8 2 6 3 5 +--R y(x) + (7x + 7a)y(x) + (2x + 6b x)y(x) +--R + +--R 4 2 2 4 5 3 3 +--R (15x + 30a x + 15a )y(x) + (8x + (24b + 8a)x + 24a b x)y(x) +--R + +--R 6 4 2 2 2 3 2 +--R (10x + (6b + 27a)x + (9b + 27a + 9)x + 9a + 9a)y(x) +--R + +--R 7 5 2 3 2 8 +--R (6x + (18b + 12a)x + (36a b + 6a )x + 18a b x)y(x) + x +--R + +--R 6 2 4 2 2 2 +--R (6b + a)x + (9b + 6a b + 9)x + (9a b + 18a)x + 9a +--R * +--R , +--R y (x) +--R +--R + +--R 7 2 6 3 5 +--R 2x y(x) + (x + b)y(x) + (12x + 12a x)y(x) +--R + +--R 4 2 4 +--R (10x + (18b + 6a)x + 6a b)y(x) +--R + +--R 5 3 2 2 3 +--R (20x + (8b + 36a)x + (6b + 18a + 6)x)y(x) +--R + +--R 6 4 2 2 2 2 +--R (21x + (45b + 30a)x + (54a b + 9a )x + 9a b)y(x) +--R + +--R 7 5 2 3 2 8 +--R (8x + (36b + 6a)x + (36b + 24a b + 36)x + (18a b + 36a)x)y(x) + x +--R + +--R 6 2 4 3 2 +--R 7b x + (15b + 15)x + (9b + 27b + 9a + 9)x + (9a + 9)b +--R / +--R 9 +--R Type: Expression Integer +--E 66 + +--S 67 of 130 +ode275 := (y(x)**2+x**2+x)*D(y(x),x)-y(x) +--R +--R +--R 2 2 , +--R (66) (y(x) + x + x)y (x) - y(x) +--R +--R Type: Expression Integer +--E 67 + +--S 68 of 130 +solve(ode275,y,x) +--R +--R +--R (67) "failed" +--R Type: Union("failed",...) +--E 68 + +--S 69 of 130 +ode276 := (y(x)**2-x**2)*D(y(x),x)+2*x*y(x) +--R +--R +--R 2 2 , +--R (68) (y(x) - x )y (x) + 2x y(x) +--R +--R Type: Expression Integer +--E 69 + +--S 70 of 130 +yx:=solve(ode276,y,x) +--R +--R +--R 2 2 +--R y(x) + x +--R (69) ---------- +--R y(x) +--R Type: Union(Expression Integer,...) +--E 70 + +--S 71 of 130 +ode276expr := (yx**2-x**2)*D(yx,x)+2*x*yx +--R +--R +--R 6 6 , 5 3 3 5 +--R (y(x) - x )y (x) + 4x y(x) + 4x y(x) + 2x y(x) +--R +--R (70) ------------------------------------------------- +--R 4 +--R y(x) +--R Type: Expression Integer +--E 71 + +--S 72 of 130 +ode277 := (y(x)**2+x**4)*D(y(x),x)-4*x**3*y(x) +--R +--R +--R 2 4 , 3 +--R (71) (y(x) + x )y (x) - 4x y(x) +--R +--R Type: Expression Integer +--E 72 + +--S 73 of 130 +yx:=solve(ode277,y,x) +--R +--R +--R 2 4 +--R y(x) - x +--R (72) ---------- +--R y(x) +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 130 +ode277expr := (yx**2+x**4)*D(yx,x)-4*x**3*yx +--R +--R +--R 6 12 , 3 5 7 3 11 +--R (y(x) + x )y (x) - 8x y(x) + 8x y(x) - 4x y(x) +--R +--R (73) --------------------------------------------------- +--R 4 +--R y(x) +--R Type: Expression Integer +--E 74 + +--S 75 of 130 +ode278 := (y(x)**2+4*sin(x))*D(y(x),x)-cos(x) +--R +--R +--R 2 , +--R (74) (4sin(x) + y(x) )y (x) - cos(x) +--R +--R Type: Expression Integer +--E 75 + +--S 76 of 130 +yx:=solve(ode278,y,x) +--R +--R +--R 2 - 4y(x) +--R (- 32sin(x) - 8y(x) - 4y(x) - 1)%e +--R (75) ------------------------------------------ +--R 32 +--R Type: Union(Expression Integer,...) +--E 76 + +--S 77 of 130 +ode278expr := (yx**2+4*sin(x))*D(yx,x)-cos(x) +--R +--R +--R (76) +--R 3 2 2 +--R 4096sin(x) + (3072y(x) + 1024y(x) + 256)sin(x) +--R + +--R 4 3 2 6 +--R (768y(x) + 512y(x) + 192y(x) + 32y(x) + 4)sin(x) + 64y(x) +--R + +--R 5 4 3 2 +--R 64y(x) + 32y(x) + 8y(x) + y(x) +--R * +--R - 4y(x) 3 +--R (%e ) +--R + +--R 2 2 - 4y(x) +--R (16384sin(x) + 4096y(x) sin(x))%e +--R * +--R , +--R y (x) +--R +--R + +--R 2 2 +--R - 1024cos(x)sin(x) + (- 512y(x) - 256y(x) - 64)cos(x)sin(x) +--R + +--R 4 3 2 +--R (- 64y(x) - 64y(x) - 32y(x) - 8y(x) - 1)cos(x) +--R * +--R - 4y(x) 3 +--R (%e ) +--R + +--R - 4y(x) +--R - 4096cos(x)sin(x)%e - 1024cos(x) +--R / +--R 1024 +--R Type: Expression Integer +--E 77 + +--S 78 of 130 +ode279 := (y(x)**2+2*y(x)+x)*D(y(x),x)+(y(x)+x)**2*y(x)**2+y(x)*(y(x)+1) +--R +--R +--R 2 , 4 3 2 2 +--R (77) (y(x) + 2y(x) + x)y (x) + y(x) + 2x y(x) + (x + 1)y(x) + y(x) +--R +--R Type: Expression Integer +--E 78 + +--S 79 of 130 +solve(ode279,y,x) +--R +--R +--R (78) "failed" +--R Type: Union("failed",...) +--E 79 + +--S 80 of 130 +ode280 := (y(x)+x)**2*D(y(x),x)-a**2 +--R +--R +--R 2 2 , 2 +--R (79) (y(x) + 2x y(x) + x )y (x) - a +--R +--R Type: Expression Integer +--E 80 + +--S 81 of 130 +solve(ode280,y,x) +--R +--R +--R (80) "failed" +--R Type: Union("failed",...) +--E 81 + +--S 82 of 130 +ode281 := (y(x)**2+2*x*y(x)-x**2)*D(y(x),x)-_ + y(x)**2+2*x*y(x)+x**2 +--R +--R +--R 2 2 , 2 2 +--R (81) (y(x) + 2x y(x) - x )y (x) - y(x) + 2x y(x) + x +--R +--R Type: Expression Integer +--E 82 + +--S 83 of 130 +solve(ode281,y,x) +--R +--R +--R (82) "failed" +--R Type: Union("failed",...) +--E 83 + +--S 84 of 130 +ode282 := (y(x)+3*x-1)**2*D(y(x),x)-(2*y(x)-1)*(4*y(x)+6*x-3) +--R +--R +--R (83) +--R 2 2 , 2 +--R (y(x) + (6x - 2)y(x) + 9x - 6x + 1)y (x) - 8y(x) + (- 12x + 10)y(x) + 6x +--R +--R + +--R - 3 +--R Type: Expression Integer +--E 84 + +--S 85 of 130 +solve(ode282,y,x) +--R +--R +--R (84) "failed" +--R Type: Union("failed",...) +--E 85 + +--S 86 of 130 +ode283 := 3*(y(x)**2-x**2)*D(y(x),x)+2*y(x)**3-6*x*(x+1)*y(x)-3*exp(x) +--R +--R +--R 2 2 , x 3 2 +--R (85) (3y(x) - 3x )y (x) - 3%e + 2y(x) + (- 6x - 6x)y(x) +--R +--R Type: Expression Integer +--E 86 + +--S 87 of 130 +yx:=solve(ode283,y,x) +--R +--R +--R x 3 3 2 x 2 +--R (86) - (%e ) + (y(x) - 3x y(x))(%e ) +--R Type: Union(Expression Integer,...) +--E 87 + +--S 88 of 130 +ode283expr := 3*(yx**2-x**2)*D(yx,x)+2*yx**3-6*x*(x+1)*yx-3*exp(x) +--R +--R +--R (87) +--R 2 2 x 8 5 2 3 4 x 7 +--R (9y(x) - 9x )(%e ) + (- 18y(x) + 72x y(x) - 54x y(x))(%e ) +--R + +--R 8 2 6 4 4 6 2 x 6 +--R (9y(x) - 63x y(x) + 135x y(x) - 81x y(x) )(%e ) +--R + +--R 2 2 4 x 2 +--R (- 9x y(x) + 9x )(%e ) +--R * +--R , +--R y (x) +--R +--R + +--R x 9 3 2 x 8 +--R - 11(%e ) + (30y(x) + (- 90x - 18x)y(x))(%e ) +--R + +--R 6 2 4 4 3 2 x 7 +--R (- 27y(x) + (162x + 36x)y(x) + (- 243x - 108x )y(x) )(%e ) +--R + +--R 9 2 7 4 3 5 +--R 8y(x) + (- 72x - 18x)y(x) + (216x + 108x )y(x) +--R + +--R 6 5 3 +--R (- 216x - 162x )y(x) +--R * +--R x 6 +--R (%e ) +--R + +--R 2 x 3 2 3 4 3 x 2 x +--R (15x + 6x)(%e ) + ((- 12x - 6x)y(x) + (36x + 36x )y(x))(%e ) - 3%e +--R Type: Expression Integer +--E 88 + +--S 89 of 130 +ode284 := (4*y(x)**2+x**2)*D(y(x),x)-x*y(x) +--R +--R +--R 2 2 , +--R (88) (4y(x) + x )y (x) - x y(x) +--R +--R Type: Expression Integer +--E 89 + +--S 90 of 130 +yx:=solve(ode284,y,x) +--R +--R +--R 2 2 +--R 8y(x) log(y(x)) - x +--R (89) -------------------- +--R 2 +--R 2y(x) +--R Type: Union(Expression Integer,...) +--E 90 + +--S 91 of 130 +ode284expr := (4*yx**2+x**2)*D(yx,x)-x*yx +--R +--R +--R (90) +--R 6 2 4 2 +--R (512y(x) + 128x y(x) )log(y(x)) +--R + +--R 2 4 4 2 2 6 4 4 4 2 +--R (- 128x y(x) - 32x y(x) )log(y(x)) + 8x y(x) + 2x y(x) + 8x y(x) +--R + +--R 6 +--R 2x +--R * +--R , +--R y (x) +--R +--R + +--R 5 2 7 3 3 3 5 +--R - 128x y(x) log(y(x)) + (- 8x y(x) + 32x y(x) )log(y(x)) - x y(x) +--R + +--R 5 +--R - 2x y(x) +--R / +--R 7 +--R 2y(x) +--R Type: Expression Integer +--E 91 + +--S 92 of 130 +ode285 := (4*y(x)**2+2*x*y(x)+3*x**2)*D(y(x),x)+y(x)**2+6*x*y(x)+2*x**2 +--R +--R +--R 2 2 , 2 2 +--R (91) (4y(x) + 2x y(x) + 3x )y (x) + y(x) + 6x y(x) + 2x +--R +--R Type: Expression Integer +--E 92 + +--S 93 of 130 +yx:=solve(ode285,y,x) +--R +--R +--R 3 2 2 3 +--R 4y(x) + 3x y(x) + 9x y(x) + 2x +--R (92) --------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 93 + +--S 94 of 130 +ode285expr := (4*yx**2+2*x*yx+3*x**2)*D(yx,x)+yx**2+6*x*yx+2*x**2 +--R +--R +--R (93) +--R 8 7 2 6 3 5 +--R 256y(x) + 512x y(x) + 1680x y(x) + (2056x + 96x)y(x) +--R + +--R 4 2 4 5 3 3 +--R (3020x + 120x )y(x) + (2160x + 324x )y(x) +--R + +--R 6 4 2 2 7 5 3 8 +--R (1468x + 210x + 108x )y(x) + (464x + 186x + 54x )y(x) + 48x +--R + +--R 6 4 +--R 36x + 81x +--R * +--R , +--R y (x) +--R +--R + +--R 8 7 2 6 3 5 +--R 64y(x) + 480x y(x) + (1028x + 16)y(x) + (2416x + 48x)y(x) +--R + +--R 4 2 4 5 3 3 +--R (2700x + 243x )y(x) + (2936x + 280x + 72x)y(x) +--R + +--R 6 4 2 2 7 5 3 8 6 +--R (1624x + 465x + 81x )y(x) + (384x + 216x + 324x )y(x) + 32x + 28x +--R + +--R 4 2 +--R 90x + 18x +--R / +--R 9 +--R Type: Expression Integer +--E 94 + +--S 95 of 130 +ode286 := (2*y(x)-3*x+1)**2*D(y(x),x)-(3*y(x)-2*x-4)**2 +--R +--R +--R (94) +--R 2 2 , 2 +--R (4y(x) + (- 12x + 4)y(x) + 9x - 6x + 1)y (x) - 9y(x) + (12x + 24)y(x) +--R +--R + +--R 2 +--R - 4x - 16x - 16 +--R Type: Expression Integer +--E 95 + +--S 96 of 130 +solve(ode286,y,x) +--R +--R +--R (95) "failed" +--R Type: Union("failed",...) +--E 96 + +--S 97 of 130 +ode287 := (2*y(x)-4*x+1)**2*D(y(x),x)-(y(x)-2*x)**2 +--R +--R +--R (96) +--R 2 2 , 2 2 +--R (4y(x) + (- 16x + 4)y(x) + 16x - 8x + 1)y (x) - y(x) + 4x y(x) - 4x +--R +--R Type: Expression Integer +--E 97 + +--S 98 of 130 +solve(ode287,y,x) +--R +--R +--R (97) "failed" +--R Type: Union("failed",...) +--E 98 + +--S 99 of 130 +ode288 := (6*y(x)**2-3*x**2*y(x)+1)*D(y(x),x)-3*x*y(x)**2+x +--R +--R +--R 2 2 , 2 +--R (98) (6y(x) - 3x y(x) + 1)y (x) - 3x y(x) + x +--R +--R Type: Expression Integer +--E 99 + +--S 100 of 130 +yx:=solve(ode288,y,x) +--R +--R +--R 3 2 2 2 +--R 4y(x) - 3x y(x) + 2y(x) + x +--R (99) ------------------------------ +--R 2 +--R Type: Union(Expression Integer,...) +--E 100 + +--S 101 of 130 +ode288expr := (6*yx**2-3*x**2*yx+1)*D(yx,x)-3*x*yx**2+x +--R +--R +--R (100) +--R 8 2 7 4 6 6 2 5 +--R 576y(x) - 1152x y(x) + (756x + 672)y(x) + (- 162x - 720x )y(x) +--R + +--R 4 4 6 2 3 4 2 +--R (90x + 240)y(x) + (54x - 48x )y(x) + (- 54x + 48)y(x) + 4 +--R * +--R , +--R y (x) +--R +--R + +--R 8 3 7 5 6 3 5 +--R - 288x y(x) + 432x y(x) + (- 162x - 240x)y(x) + 72x y(x) +--R + +--R 5 4 3 3 5 +--R (81x - 24x)y(x) - 72x y(x) - 3x + 8x +--R / +--R 4 +--R Type: Expression Integer +--E 101 + +--S 102 of 130 +ode289 := (6*y(x)-x)**2*D(y(x),x)-6*y(x)**2+2*x*y(x)+a +--R +--R +--R 2 2 , 2 +--R (101) (36y(x) - 12x y(x) + x )y (x) - 6y(x) + 2x y(x) + a +--R +--R Type: Expression Integer +--E 102 + +--S 103 of 130 +yx:=solve(ode289,y,x) +--R +--R +--R 3 2 2 +--R (102) 12y(x) - 6x y(x) + x y(x) + a x +--R Type: Union(Expression Integer,...) +--E 103 + +--S 104 of 130 +ode289expr := (6*yx-x)**2*D(yx,x)-6*yx**2+2*x*yx+a +--R +--R +--R (103) +--R 8 7 2 6 +--R 186624y(x) - 248832x y(x) + 145152x y(x) +--R + +--R 3 5 +--R (- 46656x + (31104a - 5184)x)y(x) +--R + +--R 4 2 4 5 3 3 +--R (8640x + (- 25920a + 4320)x )y(x) + (- 864x + (8640a - 1440)x )y(x) +--R + +--R 6 4 2 2 2 +--R (36x + (- 1296a + 216)x + (1296a - 432a + 36)x )y(x) +--R + +--R 5 2 3 2 4 +--R ((72a - 12)x + (- 432a + 144a - 12)x )y(x) + (36a - 12a + 1)x +--R * +--R , +--R y (x) +--R +--R + +--R 8 7 2 6 +--R - 31104y(x) + 41472x y(x) + (- 23328x + 5184a - 864)y(x) +--R + +--R 3 5 4 2 4 +--R (6912x + (- 10368a + 1728)x)y(x) + (- 1080x + (6480a - 1080)x )y(x) +--R + +--R 5 3 2 3 +--R (72x + (- 1728a + 288)x + (864a - 288a + 24)x)y(x) +--R + +--R 4 2 2 2 2 3 +--R ((180a - 30)x + (- 648a + 216a - 18)x )y(x) + (144a - 48a + 4)x y(x) +--R + +--R 3 2 2 +--R (36a - 18a + 3a)x + a +--R Type: Expression Integer +--E 104 + +--S 105 of 130 +ode290 := (a*y(x)**2+2*b*x*y(x)+c*x**2)*D(y(x),x)+b*y(x)**2+2*c*x*y(x)+d*x**2 +--R +--R +--R 2 2 , 2 2 +--R (104) (a y(x) + 2b x y(x) + c x )y (x) + b y(x) + 2c x y(x) + d x +--R +--R Type: Expression Integer +--E 105 + +--S 106 of 130 +yx:=solve(ode290,y,x) +--R +--R +--R 3 2 2 3 +--R a y(x) + 3b x y(x) + 3c x y(x) + d x +--R (105) --------------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 106 + +--S 107 of 130 +ode290expr:=(a*yx**2+2*b*x*yx+c*x**2)*D(yx,x)+b*yx**2+2*c*x*yx+d*x**2 +--R +--R +--R (106) +--R 4 8 3 7 3 2 2 2 6 +--R a y(x) + 8a b x y(x) + (7a c + 21a b )x y(x) +--R + +--R 3 2 3 3 2 5 +--R ((2a d + 36a b c + 18a b )x + 6a b x)y(x) +--R + +--R 2 2 2 2 4 2 2 4 +--R ((10a b d + 15a c + 45a b c)x + 30a b x )y(x) +--R + +--R 2 2 2 5 3 3 3 +--R (((8a c + 12a b )d + 36a b c )x + (24a b c + 36b )x )y(x) +--R + +--R 2 2 3 6 2 4 2 2 +--R ((a d + 18a b c d + 9a c )x + (6a b d + 54b c)x + 9a c x )y(x) +--R + +--R 2 2 7 2 2 5 3 2 8 +--R ((2a b d + 6a c d)x + (12b d + 18b c )x + 18b c x )y(x) + a c d x +--R + +--R 6 2 4 +--R 6b c d x + 9c x +--R * +--R , +--R y (x) +--R +--R + +--R 3 8 3 2 2 7 +--R a b y(x) + (2a c + 6a b )x y(x) +--R + +--R 3 2 3 2 2 6 +--R ((a d + 18a b c + 9a b )x + a b)y(x) +--R + +--R 2 2 2 2 3 2 5 +--R ((8a b d + 12a c + 36a b c)x + 12a b x)y(x) +--R + +--R 2 2 2 4 3 2 4 +--R (((10a c + 15a b )d + 45a b c )x + (18a b c + 27b )x )y(x) +--R + +--R 2 2 3 5 2 3 3 +--R ((2a d + 36a b c d + 18a c )x + (8a b d + 72b c)x + 6a c x)y(x) +--R + +--R 2 2 6 2 2 4 2 2 +--R ((7a b d + 21a c d)x + (30b d + 45b c )x + 27b c x )y(x) +--R + +--R 2 7 5 2 3 3 8 2 6 4 2 +--R (8a c d x + 36b c d x + 36c x )y(x) + a d x + 7b d x + 15c d x + 9d x +--R / +--R 9 +--R Type: Expression Integer +--E 107 + +--S 108 of 130 +ode291 := (b*(beta*y(x)+alpha*x)**2-beta*(b*y(x)+a*x))*D(y(x),x)+_ + a*(beta*y(x)+alpha*x)**2-alpha*(b*y(x)+a*x) +--R +--R +--R (107) +--R 2 2 2 2 +--R (b beta y(x) + (2alpha b beta x - b beta)y(x) + alpha b x - a beta x) +--R * +--R , +--R y (x) +--R +--R + +--R 2 2 2 2 +--R a beta y(x) + (2a alpha beta x - alpha b)y(x) + a alpha x - a alpha x +--R Type: Expression Integer +--E 108 + +--S 109 of 130 +solve(ode291,y,x) +--R +--R +--R (108) "failed" +--R Type: Union("failed",...) +--E 109 + +--S 110 of 130 +ode292 := (a*y(x)+b*x+c)**2*D(y(x),x)+(alpha*y(x)+beta*x+gamma)**2 +--R +--R +--R (109) +--R 2 2 2 2 2 , 2 2 +--R (a y(x) + (2a b x + 2a c)y(x) + b x + 2b c x + c )y (x) + alpha y(x) +--R +--R + +--R 2 2 2 +--R (2alpha beta x + 2alpha gamma)y(x) + beta x + 2beta gamma x + gamma +--R Type: Expression Integer +--E 110 + +--S 111 of 130 +solve(ode292,y,x) +--R +--R +--R (110) "failed" +--R Type: Union("failed",...) +--E 111 + +--S 112 of 130 +ode293 := x*(y(x)**2-3*x)*D(y(x),x)+2*y(x)**3-5*x*y(x) +--R +--R +--R 2 2 , 3 +--R (111) (x y(x) - 3x )y (x) + 2y(x) - 5x y(x) +--R +--R Type: Expression Integer +--E 112 + +--S 113 of 130 +solve(ode293,y,x) +--R +--R +--R (112) "failed" +--R Type: Union("failed",...) +--E 113 + +--S 114 of 130 +ode294 := x*(y(x)**2+x**2-a)*D(y(x),x)-y(x)*(y(x)**2+x**2+a) +--R +--R +--R 2 3 , 3 2 +--R (113) (x y(x) + x - a x)y (x) - y(x) + (- x - a)y(x) +--R +--R Type: Expression Integer +--E 114 + +--S 115 of 130 +solve(ode294,y,x) +--R +--R +--R (114) "failed" +--R Type: Union("failed",...) +--E 115 + +--S 116 of 130 +ode295 := x*(y(x)**2+x*y(x)-x**2)*D(y(x),x)-y(x)**3+x*y(x)**2+x**2*y(x) +--R +--R +--R 2 2 3 , 3 2 2 +--R (115) (x y(x) + x y(x) - x )y (x) - y(x) + x y(x) + x y(x) +--R +--R Type: Expression Integer +--E 116 + +--S 117 of 130 +solve(ode295,y,x) +--R +--R +--R (116) "failed" +--R Type: Union("failed",...) +--E 117 + +--S 118 of 130 +ode296 := x*(y(x)**2+x**2*y(x)+x**2)*D(y(x),x)-2*y(x)**3-2*x**2*y(x)**2+x**4 +--R +--R +--R 2 3 3 , 3 2 2 4 +--R (117) (x y(x) + x y(x) + x )y (x) - 2y(x) - 2x y(x) + x +--R +--R Type: Expression Integer +--E 118 + +--S 119 of 130 +solve(ode296,y,x) +--R +--R +--R (118) "failed" +--R Type: Union("failed",...) +--E 119 + +--S 120 of 130 +ode297 := 2*x*(y(x)**2+5*x**2)*D(y(x),x)+y(x)**3-x**2*y(x) +--R +--R +--R 2 3 , 3 2 +--R (119) (2x y(x) + 10x )y (x) + y(x) - x y(x) +--R +--R Type: Expression Integer +--E 120 + +--S 121 of 130 +solve(ode297,y,x) +--R +--R +--R (120) "failed" +--R Type: Union("failed",...) +--E 121 + +--S 122 of 130 +ode298 := 3*x*y(x)**2*D(y(x),x)+y(x)**3-2*x +--R +--R +--R 2 , 3 +--R (121) 3x y(x) y (x) + y(x) - 2x +--R +--R Type: Expression Integer +--E 122 + +--S 123 of 130 +yx:=solve(ode298,y,x) +--R +--R +--R 3 2 +--R (122) x y(x) - x +--R Type: Union(Expression Integer,...) +--E 123 + +--S 124 of 130 +ode298expr := 3*x*yx**2*D(yx,x)+yx**3-2*x +--R +--R +--R (123) +--R 4 8 5 5 6 2 , 3 9 4 6 5 3 +--R (9x y(x) - 18x y(x) + 9x y(x) )y (x) + 4x y(x) - 15x y(x) + 18x y(x) +--R +--R + +--R 6 +--R - 7x - 2x +--R Type: Expression Integer +--E 124 + +--S 125 of 130 +ode299 := (3*x*y(x)**2-x**2)*D(y(x),x)+y(x)**3-2*x*y(x) +--R +--R +--R 2 2 , 3 +--R (124) (3x y(x) - x )y (x) + y(x) - 2x y(x) +--R +--R Type: Expression Integer +--E 125 + +--S 126 of 130 +yx:=solve(ode299,y,x) +--R +--R +--R 3 2 +--R (125) x y(x) - x y(x) +--R Type: Union(Expression Integer,...) +--E 126 + +--S 127 of 130 +ode299expr := (3*x*yx**2-x**2)*D(yx,x)+yx**3-2*x*yx +--R +--R +--R (126) +--R 4 8 5 6 6 4 7 3 2 4 , +--R (9x y(x) - 21x y(x) + 15x y(x) + (- 3x - 3x )y(x) + x )y (x) +--R +--R + +--R 3 9 4 7 5 5 6 2 3 3 +--R 4x y(x) - 15x y(x) + 18x y(x) + (- 7x - 3x )y(x) + 4x y(x) +--R Type: Expression Integer +--E 127 + +--S 128 of 130 +ode300 := 6*x*y(x)**2*D(y(x),x)+2*y(x)**3+x +--R +--R +--R 2 , 3 +--R (127) 6x y(x) y (x) + 2y(x) + x +--R +--R Type: Expression Integer +--E 128 + +--S 129 of 130 +yx:=solve(ode300,y,x) +--R +--R +--R 3 2 +--R 4x y(x) + x +--R (128) ------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 129 + +--S 130 of 130 +ode300expr := 6*x*yx**2*D(yx,x)+2*yx**3+x +--R +--R +--R (129) +--R 4 8 5 5 6 2 , 3 9 4 6 +--R (576x y(x) + 288x y(x) + 36x y(x) )y (x) + 256x y(x) + 240x y(x) +--R +--R + +--R 5 3 6 +--R 72x y(x) + 7x + 4x +--R / +--R 4 +--R Type: Expression Integer +--E 130 + +)spool +)lisp (bye) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} {\bf http://www.cs.uwaterloo.ca/$\tilde{}$ecterrab/odetools.html} +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/kamke5.input.pdf b/src/axiom-website/CATS/kamke5.input.pdf new file mode 100644 index 0000000..3d07ba6 Binary files /dev/null and b/src/axiom-website/CATS/kamke5.input.pdf differ diff --git a/src/axiom-website/CATS/kamke6.input.pamphlet b/src/axiom-website/CATS/kamke6.input.pamphlet new file mode 100644 index 0000000..ad31cd3 --- /dev/null +++ b/src/axiom-website/CATS/kamke6.input.pamphlet @@ -0,0 +1,3661 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input kamke6.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This is the 301-350 of the Kamke test suite as published by +E. S. Cheb-Terrab\cite{1}. They have been rewritten using Axiom +syntax. Where possible we show that the particular solution actually +satisfies the original ordinary differential equation. +\end{abstract} +\eject +\tableofcontents +\eject +<<*>>= +)spool kamke6.output +)set break resume +)set mes auto off +)clear all + +--S 1 of 120 +y:=operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 1 + +--S 2 of 120 +--Rf:=operator 'f +--R +--R +--R (2) f +--R Type: BasicOperator +--E 2 + +--S 3 of 120 +--Rg:=operator 'g +--R +--R +--R (3) g +--R Type: BasicOperator +--R +--E 3 + +--S 4 of 120 +--Rode301 := (6*x*y(x)**2+x**2)*D(y(x),x)-y(x)*(3*y(x)**2-x) +--R +--R +--R 2 2 , 3 +--R (4) (6x y(x) + x )y (x) - 3y(x) + x y(x) +--R +--R Type: Expression Integer +--E 4 + +--S 5 of 120 +--Rsolve(ode301,y,x) +--R +--R +--R (5) "failed" +--R Type: Union("failed",...) +--E 5 + +--S 6 of 120 +--Rode302 := (x**2*y(x)**2+x)*D(y(x),x)+y(x) +--R +--R +--R 2 2 , +--R (6) (x y(x) + x)y (x) + y(x) +--R +--R Type: Expression Integer +--E 6 + +--S 7 of 120 +--Rsolve(ode302,y,x) +--R +--R +--R (7) "failed" +--R Type: Union("failed",...) +--E 7 + +--S 8 of 120 +--Rode303 := (x*y(x)-1)**2*x*D(y(x),x)+(x**2*y(x)**2+1)*y(x) +--R +--R +--R 3 2 2 , 2 3 +--R (8) (x y(x) - 2x y(x) + x)y (x) + x y(x) + y(x) +--R +--R Type: Expression Integer +--E 8 + +--S 9 of 120 +--Rsolve(ode303,y,x) +--R +--R +--R (9) "failed" +--R Type: Union("failed",...) +--E 9 + +--S 10 of 120 +--Rode304 := (10*x**3*y(x)**2+x**2*y(x)+2*x)*D(y(x),x)+5*x**2*y(x)**3+x*y(x)**2 +--R +--R +--R 3 2 2 , 2 3 2 +--R (10) (10x y(x) + x y(x) + 2x)y (x) + 5x y(x) + x y(x) +--R +--R Type: Expression Integer +--E 10 + +--S 11 of 120 +--Rsolve(ode304,y,x) +--R +--R +--R (11) "failed" +--R Type: Union("failed",...) +--E 11 + +--S 12 of 120 +--Rode305 := (y(x)**3-3*x)*D(y(x),x)-3*y(x)+x**2 +--R +--R +--R 3 , 2 +--R (12) (y(x) - 3x)y (x) - 3y(x) + x +--R +--R Type: Expression Integer +--E 12 + +--S 13 of 120 +--Ryx:=solve(ode305,y,x) +--R +--R +--R 4 3 +--R 3y(x) - 36x y(x) + 4x +--R (13) ----------------------- +--R 12 +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 120 +--Rode305expr := (yx**3-3*x)*D(yx,x)-3*yx+x**2 +--R +--R +--R (14) +--R 15 12 3 11 2 9 4 8 +--R 27y(x) - 1053x y(x) + 108x y(x) + 14580x y(x) - 2916x y(x) +--R + +--R 6 7 3 6 5 5 7 4 +--R 144x y(x) - 81648x y(x) + 23328x y(x) - 2160x y(x) +--R + +--R 9 4 3 6 2 8 10 +--R (64x + 139968x - 5184x)y(x) - 46656x y(x) + 5184x y(x) - 192x +--R + +--R 2 +--R 15552x +--R * +--R , +--R y (x) +--R +--R + +--R 13 2 12 10 3 9 5 8 +--R - 81y(x) + 27x y(x) + 2916x y(x) - 1296x y(x) + 108x y(x) +--R + +--R 2 7 4 6 6 5 +--R - 34992x y(x) + 19440x y(x) - 3024x y(x) +--R + +--R 8 3 4 5 3 7 2 +--R (144x + 139968x - 1296)y(x) - 93312x y(x) + 20736x y(x) +--R + +--R 9 11 3 2 +--R (- 1920x + 31104x)y(x) + 64x - 6912x + 1728x +--R / +--R 1728 +--R Type: Expression Integer +--E 14 + +--S 15 of 120 +--Rode306 := (y(x)**3-x**3)*D(y(x),x)-x**2*y(x) +--R +--R +--R 3 3 , 2 +--R (15) (y(x) - x )y (x) - x y(x) +--R +--R Type: Expression Integer +--E 15 + +--S 16 of 120 +--Ryx:=solve(ode306,y,x) +--R +--R +--R 6 3 3 +--R y(x) - 2x y(x) +--R (16) ---------------- +--R 6 +--R Type: Union(Expression Integer,...) +--E 16 + +--S 17 of 120 +--Rode306expr := (yx**3-x**3)*D(yx,x)-x**2*yx +--R +--R +--R (17) +--R 23 3 20 6 17 9 14 12 11 +--R y(x) - 7x y(x) + 18x y(x) - 20x y(x) + 8x y(x) +--R + +--R 3 5 6 2 +--R - 216x y(x) + 216x y(x) +--R * +--R , +--R y (x) +--R +--R + +--R 2 21 5 18 8 15 11 12 2 6 5 3 +--R - x y(x) + 6x y(x) - 12x y(x) + 8x y(x) - 36x y(x) + 288x y(x) +--R / +--R 216 +--R Type: Expression Integer +--E 17 + +--S 18 of 120 +--Rode307 := (y(x)**2+x**2+a)*y(x)*D(y(x),x)+(y(x)**2+x**2-a)*x +--R +--R +--R 3 2 , 2 3 +--R (18) (y(x) + (x + a)y(x))y (x) + x y(x) + x - a x +--R +--R Type: Expression Integer +--E 18 + +--S 19 of 120 +--Ryx:=solve(ode307,y,x) +--R +--R +--R 4 2 2 4 2 +--R y(x) + (2x + 2a)y(x) + x - 2a x +--R (19) ------------------------------------ +--R 4 +--R Type: Union(Expression Integer,...) +--E 19 + +--S 20 of 120 +--Rode307expr := (yx**2+x**2+a)*yx*D(yx,x)+(yx**2+x**2-a)*x +--R +--R +--R (20) +--R 15 2 13 4 2 2 11 +--R y(x) + (7x + 7a)y(x) + (21x + 30a x + 18a )y(x) +--R + +--R 6 4 2 2 3 9 +--R (35x + 45a x + 30a x + 20a )y(x) +--R + +--R 8 6 2 4 3 2 4 7 +--R (35x + 20a x - 12a x + (- 16a + 16)x + 8a + 16a)y(x) +--R + +--R 10 8 2 6 3 4 4 2 +--R 21x - 15a x - 36a x + (- 24a + 48)x + (- 24a + 96a)x +--R + +--R 2 +--R 48a +--R * +--R 5 +--R y(x) +--R + +--R 12 10 2 8 3 6 4 4 2 2 +--R 7x - 18a x - 6a x + (16a + 48)x + (24a + 80a)x + 64a x +--R + +--R 3 +--R 32a +--R * +--R 3 +--R y(x) +--R + +--R 14 12 2 10 3 8 4 6 2 4 3 2 +--R (x - 5a x + 6a x + (4a + 16)x - 8a x - 48a x - 32a x )y(x) +--R * +--R , +--R y (x) +--R +--R + +--R 14 3 12 5 3 2 10 +--R x y(x) + (7x + 5a x)y(x) + (21x + 18a x + 6a x)y(x) +--R + +--R 7 5 2 3 3 8 +--R (35x + 15a x - 6a x + (- 4a + 4)x)y(x) +--R + +--R 9 7 2 5 3 3 4 6 +--R (35x - 20a x - 36a x + (- 16a + 32)x + (- 8a + 32a)x)y(x) +--R + +--R 11 9 2 7 3 5 4 3 2 4 +--R (21x - 45a x - 12a x + (24a + 72)x + (24a + 80a)x + 32a x)y(x) +--R + +--R 13 11 2 9 3 7 4 5 2 3 3 2 +--R (7x - 30a x + 30a x + (16a + 64)x - 24a x - 96a x - 32a x)y(x) +--R + +--R 15 13 2 11 3 9 4 7 3 3 +--R x - 7a x + 18a x + (- 20a + 20)x + (8a - 48a)x + (32a + 64)x +--R + +--R - 64a x +--R / +--R 64 +--R Type: Expression Integer +--E 20 + +--S 21 of 120 +--Rode308 := 2*y(x)**3*D(y(x),x)+x*y(x)**2 +--R +--R +--R 3 , 2 +--R (21) 2y(x) y (x) + x y(x) +--R +--R Type: Expression Integer +--E 21 + +--S 22 of 120 +--Ryx:=solve(ode308,y,x) +--R +--R +--R 2 2 +--R 2y(x) + x +--R (22) ----------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 22 + +--S 23 of 120 +--Rode308expr := 2*yx**3*D(yx,x)+x*yx**2 +--R +--R +--R (23) +--R 7 2 5 4 3 6 , 6 +--R (16y(x) + 24x y(x) + 12x y(x) + 2x y(x))y (x) + 8x y(x) +--R +--R + +--R 3 4 5 3 2 7 5 +--R (12x + 4x)y(x) + (6x + 4x )y(x) + x + x +--R / +--R 4 +--R Type: Expression Integer +--E 23 + +--S 24 of 120 +--Rode309 := (2*y(x)**3+y(x))*D(y(x),x)-2*x**3-x +--R +--R +--R 3 , 3 +--R (24) (2y(x) + y(x))y (x) - 2x - x +--R +--R Type: Expression Integer +--E 24 + +--S 25 of 120 +--Ryx:=solve(ode309,y,x) +--R +--R +--R 4 2 4 2 +--R y(x) + y(x) - x - x +--R (25) ----------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 25 + +--S 26 of 120 +--Rode309expr := (2*yx**3+yx)*D(yx,x)-2*x**3-x +--R +--R +--R (26) +--R 15 13 4 2 11 +--R 2y(x) + 7y(x) + (- 6x - 6x + 9)y(x) +--R + +--R 4 2 9 8 6 4 2 7 +--R (- 15x - 15x + 5)y(x) + (6x + 12x - 6x - 12x + 5)y(x) +--R + +--R 8 6 4 2 5 +--R (9x + 18x + 6x - 3x + 6)y(x) +--R + +--R 12 10 8 6 4 2 3 +--R (- 2x - 6x - 3x + 4x - x - 4x + 2)y(x) +--R + +--R 12 10 8 6 4 2 +--R (- x - 3x - 3x - x - 2x - 2x )y(x) +--R * +--R , +--R y (x) +--R +--R + +--R 3 12 3 10 7 5 3 8 +--R (- 2x - x)y(x) + (- 6x - 3x)y(x) + (6x + 9x - 3x - 3x)y(x) +--R + +--R 7 5 3 6 11 9 7 5 3 4 +--R (12x + 18x + 4x - x)y(x) + (- 6x - 15x - 6x + 6x - x - 2x)y(x) +--R + +--R 11 9 7 5 3 2 15 13 11 9 +--R (- 6x - 15x - 12x - 3x - 4x - 2x)y(x) + 2x + 7x + 9x + 5x +--R + +--R 7 5 3 +--R 5x + 6x - 6x - 4x +--R / +--R 4 +--R Type: Expression Integer +--E 26 + +--S 27 of 120 +--Rode310 := (2*y(x)**3+5*x**2*y(x))*D(y(x),x)+5*x*y(x)**2+x**3 +--R +--R +--R 3 2 , 2 3 +--R (27) (2y(x) + 5x y(x))y (x) + 5x y(x) + x +--R +--R Type: Expression Integer +--E 27 + +--S 28 of 120 +--Ryx:=solve(ode310,y,x) +--R +--R +--R 4 2 2 4 +--R 2y(x) + 10x y(x) + x +--R (28) ----------------------- +--R 4 +--R Type: Union(Expression Integer,...) +--E 28 + +--S 29 of 120 +--Rode310expr := (2*yx**3+5*x**2*yx)*D(yx,x)+5*x*yx**2+x**3 +--R +--R +--R (29) +--R 15 2 13 4 11 6 9 +--R 16y(x) + 280x y(x) + 1824x y(x) + 5300x y(x) +--R + +--R 8 2 7 10 4 5 +--R (6212x + 160x )y(x) + (1590x + 1200x )y(x) +--R + +--R 12 6 3 14 8 +--R (152x + 2080x )y(x) + (5x + 200x )y(x) +--R * +--R , +--R y (x) +--R +--R + +--R 14 3 12 5 10 7 8 +--R 40x y(x) + 608x y(x) + 3180x y(x) + (6212x + 40x)y(x) +--R + +--R 9 3 6 11 5 4 13 7 2 +--R (2650x + 800x )y(x) + (456x + 3120x )y(x) + (35x + 800x )y(x) +--R + +--R 15 9 3 +--R x + 50x + 32x +--R / +--R 32 +--R Type: Expression Integer +--E 29 + +--S 30 of 120 +--Rode311 := (20*y(x)**3-3*x*y(x)**2+6*x**2*y(x)+3*x**3)*D(y(x),x)-_ +--R y(x)**3+6*x*y(x)**2+9*x**2*y(x)+4*x**3 +--R +--R +--R (30) +--R 3 2 2 3 , 3 2 2 3 +--R (20y(x) - 3x y(x) + 6x y(x) + 3x )y (x) - y(x) + 6x y(x) + 9x y(x) + 4x +--R +--R Type: Expression Integer +--E 30 + +--S 31 of 120 +--Ryx:=solve(ode311,y,x) +--R +--R +--R 4 3 2 2 3 4 +--R (31) 5y(x) - x y(x) + 3x y(x) + 3x y(x) + x +--R Type: Union(Expression Integer,...) +--E 31 + +--S 32 of 120 +--Rode311expr := (20*yx**3-3*x*yx**2+6*x**2*yx+3*x**3)*D(yx,x)-_ +--R yx**3+6*x*yx**2+9*x**2*yx+4*x**3 +--R +--R +--R (32) +--R 15 14 2 13 3 12 +--R 50000y(x) - 37500x y(x) + 115500x y(x) + 37700x y(x) +--R + +--R 4 11 5 2 10 +--R (67860x - 1500x)y(x) + (111540x + 825x )y(x) +--R + +--R 6 3 9 7 4 8 +--R (90600x - 2400x )y(x) + (72720x - 1206x )y(x) +--R + +--R 8 5 2 7 9 6 3 6 +--R (71880x - 1032x + 600x )y(x) + (52080x - 1554x - 210x )y(x) +--R + +--R 10 7 4 5 11 8 5 4 +--R (29880x - 1206x + 558x )y(x) + (17100x - 630x + 360x )y(x) +--R + +--R 12 9 6 3 3 +--R (8860x - 420x + 156x + 60x )y(x) +--R + +--R 13 10 7 4 2 +--R (3180x - 234x + 144x - 9x )y(x) +--R + +--R 14 11 8 5 15 12 9 6 +--R (660x - 72x + 90x + 18x )y(x) + 60x - 9x + 18x + 9x +--R * +--R , +--R y (x) +--R +--R + +--R 15 14 2 13 3 12 +--R - 2500y(x) + 16500x y(x) + 8700x y(x) + (22620x - 125)y(x) +--R + +--R 4 11 5 2 10 6 3 9 +--R (50700x + 150x)y(x) + (54360x - 720x )y(x) + (56560x - 536x )y(x) +--R + +--R 7 4 8 8 5 2 7 +--R (71880x - 645x + 150x)y(x) + (66960x - 1332x - 90x )y(x) +--R + +--R 9 6 3 6 10 7 4 5 +--R (49800x - 1407x + 372x )y(x) + (37620x - 1008x + 360x )y(x) +--R + +--R 11 8 5 2 4 +--R (26580x - 945x + 234x + 45x )y(x) +--R + +--R 12 9 6 3 3 +--R (13780x - 780x + 336x - 12x )y(x) +--R + +--R 13 10 7 4 2 +--R (4620x - 396x + 360x + 45x )y(x) +--R + +--R 14 11 8 5 15 12 9 6 3 +--R (900x - 108x + 162x + 54x )y(x) + 80x - 13x + 30x + 21x + 4x +--R Type: Expression Integer +--E 32 + +--S 33 of 120 +--Rode312 := (y(x)**2/b+x**2/a)*(y(x)*D(y(x),x)+x)+((a-b)/(a+b))*_ +--R (y(x)*D(y(x),x)-x) +--R +--R +--R (33) +--R 2 3 2 2 2 2 , +--R ((a b + a )y(x) + ((b + a b)x - a b + a b)y(x))y (x) +--R +--R + +--R 2 2 2 3 2 2 +--R (a b + a )x y(x) + (b + a b)x + (a b - a b)x +--R / +--R 2 2 +--R a b + a b +--R Type: Expression Integer +--E 33 + +--S 34 of 120 +--Rsolve(ode312,y,x) +--R +--R +--R (34) "failed" +--R Type: Union("failed",...) +--E 34 + +--S 35 of 120 +--Rode313 := (2*a*y(x)**3+3*a*x*y(x)**2-b*x**3+c*x**2)*D(y(x),x)-_ +--R a*y(x)**3+c*y(x)**2+3*b*x**2*y(x)+2*b*x**3 +--R +--R +--R (35) +--R 3 2 3 2 , 3 2 2 +--R (2a y(x) + 3a x y(x) - b x + c x )y (x) - a y(x) + c y(x) + 3b x y(x) +--R +--R + +--R 3 +--R 2b x +--R Type: Expression Integer +--E 35 + +--S 36 of 120 +--Rsolve(ode313,y,x) +--R +--R +--R (36) "failed" +--R Type: Union("failed",...) +--E 36 + +--S 37 of 120 +--Rode314 := x*y(x)**3*D(y(x),x)+y(x)**4-x*sin(x) +--R +--R +--R 3 , 4 +--R (37) x y(x) y (x) - x sin(x) + y(x) +--R +--R Type: Expression Integer +--E 37 + +--S 38 of 120 +--Ryx:=solve(ode314,y,x) +--R +--R +--R 3 4 2 4 4 +--R (- 16x + 96x)sin(x) + (4x - 48x + 96)cos(x) + x y(x) +--R (38) -------------------------------------------------------- +--R 4 +--R Type: Union(Expression Integer,...) +--E 38 + +--S 39 of 120 +--Rode314expr := x*yx**3*D(yx,x)+yx**4-x*sin(x) +--R +--R +--R (39) +--R 14 12 10 8 3 3 +--R (- 16384x + 294912x - 1769472x + 3538944x )y(x) sin(x) +--R + +--R 15 13 11 9 7 +--R (12288x - 294912x + 2506752x - 8847360x + 10616832x ) +--R * +--R 3 +--R y(x) cos(x) +--R + +--R 15 13 11 7 +--R (3072x - 36864x + 110592x )y(x) +--R * +--R 2 +--R sin(x) +--R + +--R 16 14 12 10 8 +--R - 3072x + 92160x - 1032192x + 5308416x - 12386304x +--R + +--R 6 +--R 10616832x +--R * +--R 3 2 +--R y(x) cos(x) +--R + +--R 16 14 12 10 7 +--R (- 1536x + 27648x - 147456x + 221184x )y(x) cos(x) +--R + +--R 16 14 11 +--R (- 192x + 1152x )y(x) +--R * +--R sin(x) +--R + +--R 17 15 13 11 9 7 +--R 256x - 9216x + 129024x - 884736x + 3096576x - 5308416x +--R + +--R 5 +--R 3538944x +--R * +--R 3 3 +--R y(x) cos(x) +--R + +--R 17 15 13 11 9 7 2 +--R (192x - 4608x + 36864x - 110592x + 110592x )y(x) cos(x) +--R + +--R 17 15 13 11 17 15 +--R (48x - 576x + 1152x )y(x) cos(x) + 4x y(x) +--R * +--R , +--R y (x) +--R +--R + +--R 14 12 10 8 6 +--R 16384x - 229376x + 196608x + 10616832x - 56623104x +--R + +--R 4 +--R 84934656x +--R * +--R 4 +--R sin(x) +--R + +--R 15 13 11 9 7 +--R - 12288x + 229376x - 540672x - 13959168x + 116785152x +--R + +--R 5 3 +--R - 339738624x + 339738624x +--R * +--R cos(x) +--R + +--R 15 13 11 9 7 4 +--R (- 3072x + 4096x + 479232x - 3538944x + 7077888x )y(x) +--R * +--R 3 +--R sin(x) +--R + +--R 16 14 12 10 8 +--R 3072x - 67584x + 147456x + 7372800x - 79626240x +--R + +--R 6 4 2 +--R 343277568x - 679477248x + 509607936x +--R * +--R 2 +--R cos(x) +--R + +--R 16 14 12 10 8 +--R 1536x - 3072x - 442368x + 4792320x - 17694720x +--R + +--R 6 +--R 21233664x +--R * +--R 4 +--R y(x) cos(x) +--R + +--R 16 14 12 10 8 +--R (192x + 3456x - 55296x + 165888x )y(x) +--R * +--R 2 +--R sin(x) +--R + +--R 17 15 13 11 9 +--R - 256x + 5120x + 43008x - 2064384x + 23445504x +--R + +--R 7 5 3 +--R - 129171456x + 378667008x - 566231040x + 339738624x +--R * +--R 3 +--R cos(x) +--R + +--R 17 15 13 11 9 +--R - 192x - 1536x + 147456x - 1953792x + 10506240x +--R + +--R 7 5 +--R - 24772608x + 21233664x +--R * +--R 4 2 +--R y(x) cos(x) +--R + +--R 17 15 13 11 9 8 +--R (- 48x - 1728x + 40320x - 221184x + 331776x )y(x) cos(x) +--R + +--R 17 15 13 12 +--R (- 4x - 256x + 1536x )y(x) - 256x +--R * +--R sin(x) +--R + +--R 16 14 12 10 8 6 +--R 256x - 12288x + 245760x - 2654208x + 16809984x - 63700992x +--R + +--R 4 2 +--R 141557760x - 169869312x + 84934656 +--R * +--R 4 +--R cos(x) +--R + +--R 16 14 12 10 8 6 +--R 512x - 18432x + 258048x - 1769472x + 6193152x - 10616832x +--R + +--R 4 +--R 7077888x +--R * +--R 4 3 +--R y(x) cos(x) +--R + +--R 16 14 12 10 8 8 2 +--R (288x - 6912x + 55296x - 165888x + 165888x )y(x) cos(x) +--R + +--R 16 14 12 12 16 16 +--R (64x - 768x + 1536x )y(x) cos(x) + 5x y(x) +--R / +--R 256 +--R Type: Expression Integer +--E 39 + +--S 40 of 120 +--Rode315 := (2*x*y(x)**3-x**4)*D(y(x),x)-y(x)**4+2*x**3*y(x) +--R +--R +--R 3 4 , 4 3 +--R (40) (2x y(x) - x )y (x) - y(x) + 2x y(x) +--R +--R Type: Expression Integer +--E 40 + +--S 41 of 120 +--Rsolve(ode315,y,x) +--R +--R +--R (41) "failed" +--R Type: Union("failed",...) +--E 41 + +--S 42 of 120 +--Rode316 := (2*x*y(x)**3+y(x))*D(y(x),x)+2*y(x)**2 +--R +--R +--R 3 , 2 +--R (42) (2x y(x) + y(x))y (x) + 2y(x) +--R +--R Type: Expression Integer +--E 42 + +--S 43 of 120 +--Ryx:=solve(ode316,y,x) +--R +--R +--R 2 +--R y(x) +--R ----- 2 +--R 2 y(x) +--R 4x %e + Ei(-----) +--R 2 +--R (43) ---------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 120 +--Rode316expr := (2*x*yx**3+yx)*D(yx,x)+2*yx**2 +--R +--R +--R (44) +--R 2 4 2 3 +--R y(x) y(x) +--R ----- 2 ----- +--R 5 2 4 2 4 2 3 y(x) 2 +--R (128x y(x) + 64x )(%e ) + (96x y(x) + 48x )Ei(-----)(%e ) +--R 2 +--R + +--R 2 2 +--R y(x) +--R 2 2 ----- +--R 3 2 2 y(x) 2 2 2 +--R ((24x y(x) + 12x )Ei(-----) + 16x y(x) + 8x)(%e ) +--R 2 +--R + +--R 2 +--R y(x) +--R 2 3 2 ----- +--R 2 2 y(x) 2 y(x) 2 +--R ((2x y(x) + x)Ei(-----) + (4x y(x) + 2)Ei(-----))%e +--R 2 2 +--R * +--R , +--R y (x) +--R +--R + +--R 2 4 2 3 +--R y(x) y(x) +--R ----- 2 ----- +--R 4 2 3 y(x) 2 +--R 128x y(x)(%e ) + 96x y(x)Ei(-----)(%e ) +--R 2 +--R + +--R 2 2 +--R y(x) +--R 2 2 ----- +--R 2 y(x) 2 2 +--R (24x y(x)Ei(-----) + (32x + 16x)y(x))(%e ) +--R 2 +--R + +--R 2 +--R y(x) +--R 2 3 2 ----- 2 2 +--R y(x) y(x) 2 y(x) +--R (2x y(x)Ei(-----) + (16x + 4)y(x)Ei(-----))%e + 2y(x)Ei(-----) +--R 2 2 2 +--R / +--R 4y(x) +--R Type: Expression Integer +--E 44 + +--S 45 of 120 +--Rode317 := (2*x*y(x)**3+x*y(x)+x**2)*D(y(x),x)+y(x)**2-x*y(x) +--R +--R +--R 3 2 , 2 +--R (45) (2x y(x) + x y(x) + x )y (x) + y(x) - x y(x) +--R +--R Type: Expression Integer +--E 45 + +--S 46 of 120 +--Rsolve(ode317,y,x) +--R +--R +--R (46) "failed" +--R Type: Union("failed",...) +--E 46 + +--S 47 of 120 +--Rode318 := (3*x*y(x)**3-4*x*y(x)+y(x))*D(y(x),x)+y(x)**2*(y(x)**2-2) +--R +--R +--R 3 , 4 2 +--R (47) (3x y(x) + (- 4x + 1)y(x))y (x) + y(x) - 2y(x) +--R +--R Type: Expression Integer +--E 47 + +--S 48 of 120 +--Ryx:=solve(ode318,y,x) +--R +--R +--R (48) +--R +---------+ +--R 4 2 | 2 5 3 +--R (- x y(x) + (2x - 1)y(x) + 2)\|y(x) - 2 + x y(x) + (- 2x + 1)y(x) +--R + +--R - 2y(x) +--R / +--R +---------+ +--R | 2 2 +--R y(x)\|y(x) - 2 - y(x) + 2 +--R Type: Union(Expression Integer,...) +--E 48 + +--S 49 of 120 +--Rode318expr := (3*x*yx**3-4*x*yx+yx)*D(yx,x)+yx**2*(yx**2-2) +--R +--R +--R (49) +--R 5 11 5 4 9 5 4 3 7 +--R 9x y(x) + (- 30x + 30x )y(x) + (24x - 96x + 36x )y(x) +--R + +--R 4 3 2 5 3 2 3 +--R (72x - 120x + 21x )y(x) + (88x - 68x + 7x)y(x) +--R + +--R 2 +--R (40x - 14x + 1)y(x) +--R * +--R , +--R y (x) +--R +--R + +--R 4 12 4 3 10 4 3 2 8 +--R 4x y(x) + (- 16x + 13x )y(x) + (16x - 52x + 15x )y(x) +--R + +--R 3 2 6 2 4 2 +--R (52x - 66x + 8x)y(x) + (72x - 38x + 2)y(x) + (44x - 8)y(x) + 8 +--R Type: Expression Integer +--E 49 + +--S 50 of 120 +--Rode319 := (7*x*y(x)**3+y(x)-5*x)*D(y(x),x)+y(x)**4-5*y(x) +--R +--R +--R 3 , 4 +--R (50) (7x y(x) + y(x) - 5x)y (x) + y(x) - 5y(x) +--R +--R Type: Expression Integer +--E 50 + +--S 51 of 120 +--Ryx:=solve(ode319,y,x) +--R +--R +--R 7 5 4 2 +--R 10x y(x) + 2y(x) - 100x y(x) - 25y(x) + 250x y(x) +--R (51) ----------------------------------------------------- +--R 10 +--R Type: Union(Expression Integer,...) +--E 51 + +--S 52 of 120 +--Rode319expr := (7*x*yx**3+yx-5*x)*D(yx,x)+yx**4-5*yx +--R +--R +--R (52) +--R 5 27 4 25 5 24 3 23 +--R 490000x y(x) + 364000x y(x) - 17500000x y(x) + 100800x y(x) +--R + +--R 4 22 5 2 21 3 20 +--R - 13685000x y(x) + (269500000x + 12320x )y(x) - 3969000x y(x) +--R + +--R 4 19 5 2 18 +--R (210000000x + 560x)y(x) + (- 2327500000x - 505400x )y(x) +--R + +--R 3 17 4 16 +--R 60952500x y(x) + (- 1710625000x - 23800x)y(x) +--R + +--R 5 2 15 3 14 +--R (12250000000x + 7784000x )y(x) - 464625000x y(x) +--R + +--R 4 2 13 +--R (7962500000x + 70000x + 367500x)y(x) +--R + +--R 5 2 12 3 11 +--R (- 39812500000x - 55168750x )y(x) + (1842750000x + 24000x)y(x) +--R + +--R 4 2 10 +--R (- 20934375000x - 1100000x - 2406250x)y(x) +--R + +--R 5 2 9 +--R (76562500000x + 175000000x + 2000)y(x) +--R + +--R 3 8 +--R (- 3543750000x - 405000x)y(x) +--R + +--R 4 2 7 +--R (28000000000x + 6000000x + 5468750x)y(x) +--R + +--R 5 2 6 +--R (- 76562500000x - 191756250x - 35000)y(x) +--R + +--R 3 5 +--R (2460937500x + 1800000x)y(x) +--R + +--R 4 2 4 +--R (- 13671875000x - 12500000x - 50000x)y(x) +--R + +--R 5 2 3 2 +--R (27343750000x + 2000000x + 125000)y(x) - 1875000x y(x) +--R + +--R 2 2 +--R (6250000x + 250000x)y(x) - 1250000x +--R * +--R , +--R y (x) +--R +--R + +--R 4 28 3 26 4 25 2 24 +--R 80000x y(x) + 50000x y(x) - 3200000x y(x) + 10800x y(x) +--R + +--R 3 23 4 22 2 21 +--R - 2125000x y(x) + (56000000x + 880x)y(x) - 486000x y(x) +--R + +--R 3 20 4 19 +--R (37500000x + 16)y(x) + (- 560000000x - 41800x)y(x) +--R + +--R 2 18 3 17 +--R 8707500x y(x) + (- 359375000x - 800)y(x) +--R + +--R 4 16 2 15 +--R (3500000000x + 764500x)y(x) - 79650000x y(x) +--R + +--R 3 14 +--R (2031250000x + 10000x + 15000)y(x) +--R + +--R 4 13 2 12 +--R (- 14000000000x - 6668750x)y(x) + (394875000x + 2000)y(x) +--R + +--R 3 11 +--R (- 6796875000x - 200000x - 125000)y(x) +--R + +--R 4 10 2 9 +--R (35000000000x + 27500000x)y(x) + (- 1012500000x - 45000)y(x) +--R + +--R 3 8 +--R (12500000000x + 1500000x + 390625)y(x) +--R + +--R 4 7 2 6 +--R (- 50000000000x - 43068750x)y(x) + (1054687500x + 300000)y(x) +--R + +--R 3 5 +--R (- 9765625000x - 5000000x - 10000)y(x) +--R + +--R 4 4 3 2 +--R (31250000000x + 1000000x)y(x) - 625000y(x) + (6250000x + 125000)y(x) +--R + +--R - 2500000x y(x) +--R / +--R 10000 +--R Type: Expression Integer +--E 52 + +--S 53 of 120 +--Rode320 := (x**2*y(x)**3+x*y(x))*D(y(x),x)-1 +--R +--R +--R 2 3 , +--R (53) (x y(x) + x y(x))y (x) - 1 +--R +--R Type: Expression Integer +--E 53 + +--S 54 of 120 +--Rsolve(ode320,y,x) +--R +--R +--R (54) "failed" +--R Type: Union("failed",...) +--E 54 + +--S 55 of 120 +--Rode321 := (2*x**2*y(x)**3+x**2*y(x)**2-2*x)*D(y(x),x)-2*y(x)-1 +--R +--R +--R 2 3 2 2 , +--R (55) (2x y(x) + x y(x) - 2x)y (x) - 2y(x) - 1 +--R +--R Type: Expression Integer +--E 55 + +--S 56 of 120 +--Rsolve(ode321,y,x) +--R +--R +--R (56) "failed" +--R Type: Union("failed",...) +--E 56 + +--S 57 of 120 +--Rode322 := (10*x**2*y(x)**3-3*y(x)**2-2)*D(y(x),x)+5*x*y(x)**4+x +--R +--R +--R 2 3 2 , 4 +--R (57) (10x y(x) - 3y(x) - 2)y (x) + 5x y(x) + x +--R +--R Type: Expression Integer +--E 57 + +--S 58 of 120 +--Ryx:=solve(ode322,y,x) +--R +--R +--R 2 4 3 2 +--R 5x y(x) - 2y(x) - 4y(x) + x +--R (58) ------------------------------ +--R 2 +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 of 120 +--Rode322expr := (10*x**2*yx**3-3*yx**2-2)*D(yx,x)+5*x*yx**4+x +--R +--R +--R (59) +--R 10 15 8 14 6 13 +--R 25000x y(x) - 37500x y(x) + 21000x y(x) +--R + +--R 8 4 12 10 6 2 11 +--R (- 65000x - 5200x )y(x) + (15000x + 69000x + 480x )y(x) +--R + +--R 8 4 10 6 2 9 +--R (- 16500x - 23100x )y(x) + (66000x + 2000x )y(x) +--R + +--R 8 4 8 10 6 2 7 +--R (- 27000x - 38520x + 144)y(x) + (3000x + 18000x + 3840x )y(x) +--R + +--R 8 4 6 6 2 5 +--R (- 2100x - 24920x + 672)y(x) + (14760x + 4656x )y(x) +--R + +--R 8 4 4 10 6 2 3 +--R (- 3000x - 3600x + 960)y(x) + (200x + 840x + 1856x )y(x) +--R + +--R 8 4 2 6 2 8 4 +--R (- 60x - 1884x + 480)y(x) + (480x - 192x )y(x) - 40x + 24x + 64 +--R * +--R , +--R y (x) +--R +--R + +--R 9 16 7 15 5 14 7 3 13 +--R 15625x y(x) - 20000x y(x) + 9000x y(x) + (- 40000x - 1600x )y(x) +--R + +--R 9 5 12 7 3 11 +--R (12500x + 34500x + 80x)y(x) + (- 12000x - 8400x )y(x) +--R + +--R 5 10 7 3 9 +--R (39600x + 400x)y(x) + (- 24000x - 17120x )y(x) +--R + +--R 9 5 8 7 3 7 +--R (3750x + 13500x + 960x)y(x) + (- 2400x - 14240x )y(x) +--R + +--R 5 6 7 3 5 +--R (14760x + 1552x)y(x) + (- 4800x - 2880x )y(x) +--R + +--R 9 5 4 7 3 3 +--R (500x + 1260x + 928x)y(x) + (- 160x - 2512x )y(x) +--R + +--R 5 2 7 3 9 5 +--R (1440x - 192x)y(x) + (- 320x + 96x )y(x) + 25x - 12x - 16x +--R / +--R 16 +--R Type: Expression Integer +--E 59 + +--S 60 of 120 +--Rode323 := (a*x*y(x)**3+c)*x*D(y(x),x)+(b*x**3*y(x)+c)*y(x) +--R +--R +--R 2 3 , 3 2 +--R (60) (a x y(x) + c x)y (x) + b x y(x) + c y(x) +--R +--R Type: Expression Integer +--E 60 + +--S 61 of 120 +--Rsolve(ode323,y,x) +--R +--R +--R (61) "failed" +--R Type: Union("failed",...) +--E 61 + +--S 62 of 120 +--Rode324 := (2*x**3*y(x)**3-x)*D(y(x),x)+2*x**3*y(x)**3-y(x) +--R +--R +--R 3 3 , 3 3 +--R (62) (2x y(x) - x)y (x) + 2x y(x) - y(x) +--R +--R Type: Expression Integer +--E 62 + +--S 63 of 120 +--Rsolve(ode324,y,x) +--R +--R +--R (63) "failed" +--R Type: Union("failed",...) +--E 63 + +--S 64 of 120 +--Rode325 := y(x)*(y(x)**3-2*x**3)*D(y(x),x)+(2*y(x)**3-x**3)*x +--R +--R +--R 4 3 , 3 4 +--R (64) (y(x) - 2x y(x))y (x) + 2x y(x) - x +--R +--R Type: Expression Integer +--E 64 + +--S 65 of 120 +--Rsolve(ode325,y,x) +--R +--R +--R (65) "failed" +--R Type: Union("failed",...) +--E 65 + +--S 66 of 120 +--Rode326 := y(x)*((a*y(x)+b*x)**3+b*x**3)*D(y(x),x)+x*((a*y(x)+b*x)**3+a*y(x)**3) +--R +--R +--R (66) +--R 3 4 2 3 2 2 2 3 3 , +--R (a y(x) + 3a b x y(x) + 3a b x y(x) + (b + b)x y(x))y (x) +--R +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (a + a)x y(x) + 3a b x y(x) + 3a b x y(x) + b x +--R Type: Expression Integer +--E 66 + +--S 67 of 120 +--Rsolve(ode326,y,x) +--R +--R +--R (67) "failed" +--R Type: Union("failed",...) +--E 67 + +--S 68 of 120 +--Rode327 := (x*y(x)**4+2*x**2*y(x)**3+2*y(x)+x)*D(y(x),x)+y(x)**5+y(x) +--R +--R +--R 4 2 3 , 5 +--R (68) (x y(x) + 2x y(x) + 2y(x) + x)y (x) + y(x) + y(x) +--R +--R Type: Expression Integer +--E 68 + +--S 69 of 120 +--Rsolve(ode327,y,x) +--R +--R +--R (69) "failed" +--R Type: Union("failed",...) +--E 69 + +--S 70 of 120 +--Rode328 := a*x**2*y(x)**n*D(y(x),x)-2*x*D(y(x),x)+y(x) +--R +--R +--R 2 n , +--R (70) (a x y(x) - 2x)y (x) + y(x) +--R +--R Type: Expression Integer +--E 70 + +--S 71 of 120 +--Rsolve(ode328,y,x) +--R +--R +--R (71) "failed" +--R Type: Union("failed",...) +--E 71 + +--S 72 of 120 +--Rode329 := y(x)**m*x**n*(a*x*D(y(x),x)+b*y(x))+alpha*x*D(y(x),x)+beta*y(x) +--R +--R +--R n m , n m +--R (72) (a x x y(x) + alpha x)y (x) + b y(x)x y(x) + beta y(x) +--R +--R Type: Expression Integer +--E 72 + +--S 73 of 120 +--Rsolve(ode329,y,x) +--R +--R +--R (73) "failed" +--R Type: Union("failed",...) +--E 73 + +--S 74 of 120 +--Rode330 := (f(x+y(x))+1)*D(y(x),x)+f(x+y(x)) +--R +--R +--R , +--R (74) (f(y(x) + x) + 1)y (x) + f(y(x) + x) +--R +--R Type: Expression Integer +--E 74 + +--S 75 of 120 +--Rsolve(ode330,y,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 75 + +@ +I have no idea what to do with this +\begin{verbatim} + ode331 := D(y(x),x)*convert([sum(f[nu](x)*y(x)**nu,'nu'=1..p)],+)-_ + convert([sum(g[nu](x)*y(x)**nu,'nu'=1..q)],+) +\end{verbatim} +<<*>>= +--R +--S 76 of 120 +--Rode333 := (2*x**(5/2)*y(x)**(3/2)+x**2*y(x)-x)*D(y(x),x)-_ +--R x**(3/2)*y(x)**(5/2)+x*y(x)**2-y(x) +--R +--R +--R (75) +--R 2 +-+ +----+ 2 , 2 +-+ +----+ 2 +--R (2x y(x)\|x \|y(x) + x y(x) - x)y (x) - x y(x) \|x \|y(x) + x y(x) - y(x) +--R +--R Type: Expression Integer +--E 76 + +--S 77 of 120 +--Rsolve(ode333,y,x) +--R +--R +--R (76) "failed" +--R Type: Union("failed",...) +--E 77 + +--S 78 of 120 +--Rode334 := (sqrt(y(x)+x)+1)*D(y(x),x)+1 +--R +--R +--R +--------+ , +--R (77) (\|y(x) + x + 1)y (x) + 1 +--R +--R Type: Expression Integer +--E 78 + +--S 79 of 120 +--Rsolve(ode334,y,x) +--R +--R +--R (78) "failed" +--R Type: Union("failed",...) +--E 79 + +--S 80 of 120 +--Rode335 := sqrt(y(x)**2-1)*D(y(x),x)-sqrt(x**2-1) +--R +--R +--R +---------+ +------+ +--R | 2 , | 2 +--R (79) \|y(x) - 1 y (x) - \|x - 1 +--R +--R Type: Expression Integer +--E 80 + +--S 81 of 120 +--Ryx:=solve(ode335,y,x) +--R +--R +--R (80) +--R +------+ +---------+ +--R | 2 2 | 2 +--R (4x y(x)\|x - 1 + (- 4x + 2)y(x))\|y(x) - 1 +--R + +--R +------+ +--R 2 | 2 2 2 2 +--R (- 4x y(x) + 2x)\|x - 1 + (4x - 2)y(x) - 2x + 1 +--R * +--R +---------+ +--R | 2 +--R log(\|y(x) - 1 - y(x)) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (- 4x y(x)\|x - 1 + (4x - 2)y(x))log(\|x - 1 - x) +--R + +--R +------+ +--R 3 3 | 2 2 3 +--R (- 4x y(x) + 4x y(x))\|x - 1 + (4x - 2)y(x) +--R + +--R 4 2 +--R (- 4x + 2x + 1)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R +------+ +------+ +--R 2 | 2 2 2 2 | 2 +--R ((4x y(x) - 2x)\|x - 1 + (- 4x + 2)y(x) + 2x - 1)log(\|x - 1 - x) +--R + +--R +------+ +--R 4 3 2 3 | 2 2 4 +--R (4x y(x) + (- 4x - 2x)y(x) + 2x - x)\|x - 1 + (- 4x + 2)y(x) +--R + +--R 4 2 4 2 +--R (4x - 2)y(x) - 2x + 2x +--R / +--R +------+ +---------+ +--R | 2 2 | 2 +--R (8x y(x)\|x - 1 + (- 8x + 4)y(x))\|y(x) - 1 +--R + +--R +------+ +--R 2 | 2 2 2 2 +--R (- 8x y(x) + 4x)\|x - 1 + (8x - 4)y(x) - 4x + 2 +--R Type: Union(Expression Integer,...) +--E 81 + +--S 82 of 120 +--Rode335expr := sqrt(yx**2-1)*D(yx,x)-sqrt(x**2-1) +--R +--R +--R (81) +--R 4 2 5 4 2 3 +--R (- 64x + 64x - 8)y(x) + (96x - 96x + 12)y(x) +--R + +--R 4 2 +--R (- 32x + 32x - 4)y(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 5 3 5 5 3 3 +--R (64x - 96x + 32x)y(x) + (- 96x + 144x - 48x)y(x) +--R + +--R 5 3 +--R (32x - 48x + 16x)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 4 2 6 4 2 4 +--R (64x - 64x + 8)y(x) + (- 128x + 128x - 16)y(x) +--R + +--R 4 2 2 4 2 +--R (72x - 72x + 9)y(x) - 8x + 8x - 1 +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 5 3 6 5 3 4 +--R (- 64x + 96x - 32x)y(x) + (128x - 192x + 64x)y(x) +--R + +--R 5 3 2 5 3 +--R (- 72x + 108x - 36x)y(x) + 8x - 12x + 4x +--R * +--R , +--R y (x) +--R +--R + +--R 5 3 4 5 3 2 5 +--R (64x - 96x + 32x)y(x) + (- 64x + 96x - 32x)y(x) + 8x +--R + +--R 3 +--R - 12x + 4x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 6 4 2 4 6 4 2 2 +--R (- 64x + 128x - 72x + 8)y(x) + (64x - 128x + 72x - 8)y(x) +--R + +--R 6 4 2 +--R - 8x + 16x - 9x + 1 +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 5 3 5 5 3 3 +--R (- 64x + 96x - 32x)y(x) + (96x - 144x + 48x)y(x) +--R + +--R 5 3 +--R (- 32x + 48x - 16x)y(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 6 4 2 5 6 4 2 3 +--R (64x - 128x + 72x - 8)y(x) + (- 96x + 192x - 108x + 12)y(x) +--R + +--R 6 4 2 +--R (32x - 64x + 36x - 4)y(x) +--R * +--R ROOT +--R +------+ +--R 3 3 3 | 2 +--R ((64x - 32x)y(x) + (- 32x + 16x)y(x))\|x - 1 +--R + +--R 4 2 3 4 2 +--R (- 64x + 64x - 8)y(x) + (32x - 32x + 4)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 3 4 3 2 3 +--R ((- 64x + 32x)y(x) + (64x - 32x)y(x) - 8x + 4x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 4 4 2 2 4 +--R (64x - 64x + 8)y(x) + (- 64x + 64x - 8)y(x) + 8x +--R + +--R 2 +--R - 8x + 1 +--R * +--R +---------+ 2 +--R | 2 +--R log(\|y(x) - 1 - y(x)) +--R + +--R +------+ +--R 3 3 3 | 2 +--R ((- 128x + 64x)y(x) + (64x - 32x)y(x))\|x - 1 +--R + +--R 4 2 3 4 2 +--R (128x - 128x + 16)y(x) + (- 64x + 64x - 8)y(x) +--R * +--R +------+ +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 5 5 3 +--R (- 128x + 64x)y(x) + (128x - 48x)y(x) +--R + +--R 5 3 +--R (- 64x + 48x )y(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 5 +--R (128x - 128x + 16)y(x) +--R + +--R 6 4 2 3 +--R (- 128x + 64x + 64x - 16)y(x) +--R + +--R 6 4 2 +--R (64x - 80x + 16x + 2)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 3 4 3 2 3 +--R (128x - 64x)y(x) + (- 128x + 64x)y(x) + 16x +--R + +--R - 8x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 4 4 2 2 +--R (- 128x + 128x - 16)y(x) + (128x - 128x + 16)y(x) +--R + +--R 4 2 +--R - 16x + 16x - 2 +--R * +--R +------+ +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 6 5 3 4 +--R (128x - 64x)y(x) + (- 128x - 64x + 80x)y(x) +--R + +--R 5 3 2 5 3 +--R (128x - 64x - 16x)y(x) - 16x + 16x - 2x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 6 6 2 4 +--R (- 128x + 128x - 16)y(x) + (128x - 128x + 24)y(x) +--R + +--R 6 4 2 6 4 2 +--R (- 128x + 128x - 8)y(x) + 16x - 24x + 8x +--R * +--R +---------+ +--R | 2 +--R log(\|y(x) - 1 - y(x)) +--R + +--R +------+ +--R 3 3 3 | 2 +--R ((64x - 32x)y(x) + (- 32x + 16x)y(x))\|x - 1 +--R + +--R 4 2 3 4 2 +--R (- 64x + 64x - 8)y(x) + (32x - 32x + 4)y(x) +--R * +--R +------+ 2 +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 5 5 3 +--R (128x - 64x)y(x) + (- 128x + 48x)y(x) +--R + +--R 5 3 +--R (64x - 48x )y(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 5 +--R (- 128x + 128x - 16)y(x) +--R + +--R 6 4 2 3 +--R (128x - 64x - 64x + 16)y(x) +--R + +--R 6 4 2 +--R (- 64x + 80x - 16x - 2)y(x) +--R * +--R +------+ +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 7 5 3 5 +--R (64x - 32x)y(x) + (- 128x + 32x + 32x)y(x) +--R + +--R 7 5 3 3 +--R (64x + 32x - 320x + 128x)y(x) +--R + +--R 7 5 3 +--R (- 32x + 32x + 128x - 66x)y(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 7 6 4 2 5 +--R (- 64x + 64x - 8)y(x) + (128x - 96x - 32x + 12)y(x) +--R + +--R 8 4 2 3 +--R (- 64x + 344x - 280x + 28)y(x) +--R + +--R 8 6 4 2 +--R (32x - 48x - 116x + 132x - 16)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 3 4 3 2 3 +--R ((- 64x + 32x)y(x) + (64x - 32x)y(x) - 8x + 4x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 4 4 2 2 4 +--R (64x - 64x + 8)y(x) + (- 64x + 64x - 8)y(x) + 8x +--R + +--R 2 +--R - 8x + 1 +--R * +--R +------+ 2 +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 6 5 3 4 +--R (- 128x + 64x)y(x) + (128x + 64x - 80x)y(x) +--R + +--R 5 3 2 5 3 +--R (- 128x + 64x + 16x)y(x) + 16x - 16x + 2x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 6 6 2 4 +--R (128x - 128x + 16)y(x) + (- 128x + 128x - 24)y(x) +--R + +--R 6 4 2 6 4 2 +--R (128x - 128x + 8)y(x) - 16x + 24x - 8x +--R * +--R +------+ +--R | 2 +--R log(\|x - 1 - x) +--R + +--R 3 8 5 6 +--R (- 64x + 32x)y(x) + (128x - 48x)y(x) +--R + +--R 7 5 3 4 +--R (- 64x - 96x + 344x - 116x)y(x) +--R + +--R 7 5 3 2 7 5 3 +--R (64x - 32x - 280x + 132x)y(x) - 8x + 12x + 28x - 16x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 8 6 4 2 6 +--R (64x - 64x + 8)y(x) + (- 128x + 64x + 64x - 16)y(x) +--R + +--R 8 6 4 2 4 +--R (64x + 64x - 400x + 272x - 23)y(x) +--R + +--R 8 6 4 2 2 8 6 4 +--R (- 64x + 64x + 272x - 272x + 31)y(x) + 8x - 16x - 23x +--R + +--R 2 +--R 31x - 4 +--R / +--R +------+ +--R 3 3 3 | 2 +--R ((256x - 128x)y(x) + (- 128x + 64x)y(x))\|x - 1 +--R + +--R 4 2 3 4 2 +--R (- 256x + 256x - 32)y(x) + (128x - 128x + 16)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 3 4 3 2 3 +--R ((- 256x + 128x)y(x) + (256x - 128x)y(x) - 32x + 16x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 4 4 2 2 4 +--R (256x - 256x + 32)y(x) + (- 256x + 256x - 32)y(x) + 32x +--R + +--R 2 +--R - 32x + 4 +--R + +--R 5 3 4 5 3 2 5 +--R (64x - 96x + 32x)y(x) + (- 64x + 96x - 32x)y(x) + 8x +--R + +--R 3 +--R - 12x + 4x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 6 4 2 4 6 4 2 2 +--R (- 64x + 128x - 72x + 8)y(x) + (64x - 128x + 72x - 8)y(x) +--R + +--R 6 4 2 +--R - 8x + 16x - 9x + 1 +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 5 3 5 5 3 3 +--R (- 64x + 96x - 32x)y(x) + (96x - 144x + 48x)y(x) +--R + +--R 5 3 +--R (- 32x + 48x - 16x)y(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 6 4 2 5 6 4 2 3 +--R (64x - 128x + 72x - 8)y(x) + (- 96x + 192x - 108x + 12)y(x) +--R + +--R 6 4 2 +--R (32x - 64x + 36x - 4)y(x) +--R / +--R 4 2 4 4 2 2 4 2 +--R ((64x - 64x + 8)y(x) + (- 64x + 64x - 8)y(x) + 8x - 8x + 1) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 5 3 4 5 3 2 5 3 +--R (- 64x + 96x - 32x)y(x) + (64x - 96x + 32x)y(x) - 8x + 12x - 4x +--R * +--R +---------+ +--R | 2 +--R \|y(x) - 1 +--R + +--R 4 2 5 4 2 3 +--R (- 64x + 64x - 8)y(x) + (96x - 96x + 12)y(x) +--R + +--R 4 2 +--R (- 32x + 32x - 4)y(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 5 3 5 5 3 3 +--R (64x - 96x + 32x)y(x) + (- 96x + 144x - 48x)y(x) +--R + +--R 5 3 +--R (32x - 48x + 16x)y(x) +--R Type: Expression Integer +--E 82 + +--S 83 of 120 +--Rode336 := (sqrt(y(x)**2+1)+a*x)*D(y(x),x)+sqrt(x**2+1)+a*y(x) +--R +--R +--R +---------+ +------+ +--R | 2 , | 2 +--R (82) (\|y(x) + 1 + a x)y (x) + \|x + 1 + a y(x) +--R +--R Type: Expression Integer +--E 83 + +--S 84 of 120 +--Ryx:=solve(ode336,y,x) +--R +--R +--R (83) +--R +------+ +---------+ +--R | 2 2 | 2 +--R (- 4x y(x)\|x + 1 + (4x + 2)y(x))\|y(x) + 1 +--R + +--R +------+ +--R 2 | 2 2 2 2 +--R (4x y(x) + 2x)\|x + 1 + (- 4x - 2)y(x) - 2x - 1 +--R * +--R +---------+ +--R | 2 +--R log(\|y(x) + 1 - y(x)) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (- 4x y(x)\|x + 1 + (4x + 2)y(x))log(\|x + 1 - x) +--R + +--R +------+ +--R 3 2 2 3 | 2 +--R (- 4x y(x) + 8a x y(x) + (- 4x - 4x)y(x))\|x + 1 +--R + +--R 2 3 3 2 4 2 +--R (4x + 2)y(x) + (- 8a x - 4a x)y(x) + (4x + 6x + 1)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) + 1 +--R + +--R +------+ +------+ +--R 2 | 2 2 2 2 | 2 +--R ((4x y(x) + 2x)\|x + 1 + (- 4x - 2)y(x) - 2x - 1)log(\|x + 1 - x) +--R + +--R +------+ +--R 4 2 3 3 2 2 3 | 2 +--R (4x y(x) - 8a x y(x) + (4x + 6x)y(x) - 4a x y(x) + 2x + x)\|x + 1 +--R + +--R 2 4 3 3 4 2 2 +--R (- 4x - 2)y(x) + (8a x + 4a x)y(x) + (- 4x - 8x - 2)y(x) +--R + +--R 3 4 2 +--R (4a x + 2a x)y(x) - 2x - 2x +--R / +--R +------+ +---------+ +--R | 2 2 | 2 +--R (8x y(x)\|x + 1 + (- 8x - 4)y(x))\|y(x) + 1 +--R + +--R +------+ +--R 2 | 2 2 2 2 +--R (- 8x y(x) - 4x)\|x + 1 + (8x + 4)y(x) + 4x + 2 +--R Type: Union(Expression Integer,...) +--E 84 + +--S 85 of 120 +--Rode336expr := (sqrt(yx**2+1)+a*x)*D(yx,x)+sqrt(x**2+1)+a*yx +--R +--R +--R (84) +--R 6 4 2 7 +--R (- 2048x - 3072x - 1152x - 64)y(x) +--R + +--R 7 5 3 6 +--R (2048a x + 3072a x + 1152a x + 64a x)y(x) +--R + +--R 6 4 2 5 +--R (- 4096x - 6144x - 2304x - 128)y(x) +--R + +--R 7 5 3 4 +--R (3072a x + 4608a x + 1728a x + 96a x)y(x) +--R + +--R 6 4 2 3 +--R (- 2432x - 3648x - 1368x - 76)y(x) +--R + +--R 7 5 3 2 +--R (1152a x + 1728a x + 648a x + 36a x)y(x) +--R + +--R 6 4 2 7 5 +--R (- 384x - 576x - 216x - 12)y(x) + 64a x + 96a x +--R + +--R 3 +--R 36a x + 2a x +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 7 5 3 7 +--R (2048x + 4096x + 2432x + 384x)y(x) +--R + +--R 8 6 4 2 6 +--R (- 2048a x - 4096a x - 2432a x - 384a x )y(x) +--R + +--R 7 5 3 5 +--R (4096x + 8192x + 4864x + 768x)y(x) +--R + +--R 8 6 4 2 4 +--R (- 3072a x - 6144a x - 3648a x - 576a x )y(x) +--R + +--R 7 5 3 3 +--R (2432x + 4864x + 2888x + 456x)y(x) +--R + +--R 8 6 4 2 2 +--R (- 1152a x - 2304a x - 1368a x - 216a x )y(x) +--R + +--R 7 5 3 8 6 4 +--R (384x + 768x + 456x + 72x)y(x) - 64a x - 128a x - 76a x +--R + +--R 2 +--R - 12a x +--R * +--R +---------+ +--R | 2 +--R \|y(x) + 1 +--R + +--R 6 4 2 8 +--R (2048x + 3072x + 1152x + 64)y(x) +--R + +--R 7 5 3 7 +--R (- 2048a x - 3072a x - 1152a x - 64a x)y(x) +--R + +--R 6 4 2 6 +--R (5120x + 7680x + 2880x + 160)y(x) +--R + +--R 7 5 3 5 +--R (- 4096a x - 6144a x - 2304a x - 128a x)y(x) +--R + +--R 6 4 2 4 +--R (4224x + 6336x + 2376x + 132)y(x) +--R + +--R 7 5 3 3 +--R (- 2432a x - 3648a x - 1368a x - 76a x)y(x) +--R + +--R 6 4 2 2 +--R (1216x + 1824x + 684x + 38)y(x) +--R + +--R 7 5 3 6 4 +--R (- 384a x - 576a x - 216a x - 12a x)y(x) + 64x + 96x +--R + +--R 2 +--R 36x + 2 +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 7 5 3 8 +--R (- 2048x - 4096x - 2432x - 384x)y(x) +--R + +--R 8 6 4 2 7 +--R (2048a x + 4096a x + 2432a x + 384a x )y(x) +--R + +--R 7 5 3 6 +--R (- 5120x - 10240x - 6080x - 960x)y(x) +--R + +--R 8 6 4 2 5 +--R (4096a x + 8192a x + 4864a x + 768a x )y(x) +--R + +--R 7 5 3 4 +--R (- 4224x - 8448x - 5016x - 792x)y(x) +--R + +--R 8 6 4 2 3 +--R (2432a x + 4864a x + 2888a x + 456a x )y(x) +--R + +--R 7 5 3 2 +--R (- 1216x - 2432x - 1444x - 228x)y(x) +--R + +--R 8 6 4 2 7 5 3 +--R (384a x + 768a x + 456a x + 72a x )y(x) - 64x - 128x - 76x +--R + +--R - 12x +--R * +--R , +--R y (x) +--R +--R + +--R 6 4 2 7 +--R (2048a x + 3072a x + 1152a x + 64a)y(x) +--R + +--R 7 5 3 6 +--R (- 2048x - 4096x - 2432x - 384x)y(x) +--R + +--R 6 4 2 5 +--R (3072a x + 4608a x + 1728a x + 96a)y(x) +--R + +--R 7 5 3 4 +--R (- 3072x - 6144x - 3648x - 576x)y(x) +--R + +--R 6 4 2 3 +--R (1152a x + 1728a x + 648a x + 36a)y(x) +--R + +--R 7 5 3 2 +--R (- 1152x - 2304x - 1368x - 216x)y(x) +--R + +--R 6 4 2 7 5 3 +--R (64a x + 96a x + 36a x + 2a)y(x) - 64x - 128x - 76x - 12x +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 7 5 3 7 +--R (- 2048a x - 4096a x - 2432a x - 384a x)y(x) +--R + +--R 8 6 4 2 6 +--R (2048x + 5120x + 4224x + 1216x + 64)y(x) +--R + +--R 7 5 3 5 +--R (- 3072a x - 6144a x - 3648a x - 576a x)y(x) +--R + +--R 8 6 4 2 4 +--R (3072x + 7680x + 6336x + 1824x + 96)y(x) +--R + +--R 7 5 3 3 +--R (- 1152a x - 2304a x - 1368a x - 216a x)y(x) +--R + +--R 8 6 4 2 2 +--R (1152x + 2880x + 2376x + 684x + 36)y(x) +--R + +--R 7 5 3 8 6 4 +--R (- 64a x - 128a x - 76a x - 12a x)y(x) + 64x + 160x + 132x +--R + +--R 2 +--R 38x + 2 +--R * +--R +---------+ +--R | 2 +--R \|y(x) + 1 +--R + +--R 6 4 2 8 +--R (- 2048a x - 3072a x - 1152a x - 64a)y(x) +--R + +--R 7 5 3 7 +--R (2048x + 4096x + 2432x + 384x)y(x) +--R + +--R 6 4 2 6 +--R (- 4096a x - 6144a x - 2304a x - 128a)y(x) +--R + +--R 7 5 3 5 +--R (4096x + 8192x + 4864x + 768x)y(x) +--R + +--R 6 4 2 4 +--R (- 2432a x - 3648a x - 1368a x - 76a)y(x) +--R + +--R 7 5 3 3 +--R (2432x + 4864x + 2888x + 456x)y(x) +--R + +--R 6 4 2 2 +--R (- 384a x - 576a x - 216a x - 12a)y(x) +--R + +--R 7 5 3 +--R (384x + 768x + 456x + 72x)y(x) +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 7 5 3 8 +--R (2048a x + 4096a x + 2432a x + 384a x)y(x) +--R + +--R 8 6 4 2 7 +--R (- 2048x - 5120x - 4224x - 1216x - 64)y(x) +--R + +--R 7 5 3 6 +--R (4096a x + 8192a x + 4864a x + 768a x)y(x) +--R + +--R 8 6 4 2 5 +--R (- 4096x - 10240x - 8448x - 2432x - 128)y(x) +--R + +--R 7 5 3 4 +--R (2432a x + 4864a x + 2888a x + 456a x)y(x) +--R + +--R 8 6 4 2 3 +--R (- 2432x - 6080x - 5016x - 1444x - 76)y(x) +--R + +--R 7 5 3 2 +--R (384a x + 768a x + 456a x + 72a x)y(x) +--R + +--R 8 6 4 2 +--R (- 384x - 960x - 792x - 228x - 12)y(x) +--R * +--R ROOT +--R +------+ +--R 3 3 3 | 2 +--R ((64x + 32x)y(x) + (32x + 16x)y(x))\|x + 1 +--R + +--R 4 2 3 4 2 +--R (- 64x - 64x - 8)y(x) + (- 32x - 32x - 4)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) + 1 +--R + +--R 3 4 3 2 3 +--R ((- 64x - 32x)y(x) + (- 64x - 32x)y(x) - 8x - 4x) +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 4 2 4 4 2 2 4 2 +--R (64x + 64x + 8)y(x) + (64x + 64x + 8)y(x) + 8x + 8x +--R + +--R 1 +--R * +--R +---------+ 2 +--R | 2 +--R log(\|y(x) + 1 - y(x)) +--R + +--R +------+ +--R 3 3 3 | 2 +--R ((128x + 64x)y(x) + (64x + 32x)y(x))\|x + 1 +--R + +--R 4 2 3 4 2 +--R (- 128x - 128x - 16)y(x) + (- 64x - 64x - 8)y(x) +--R * +--R +------+ +--R | 2 +--R log(\|x + 1 - x) +--R + +--R 3 5 4 2 4 +--R (128x + 64x)y(x) + (- 256a x - 128a x )y(x) +--R + +--R 5 3 3 +--R (128x + 256x + 80x)y(x) +--R + +--R 4 2 2 5 3 +--R (- 128a x - 64a x )y(x) + (64x + 80x + 16x)y(x) +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 4 2 5 +--R (- 128x - 128x - 16)y(x) +--R + +--R 5 3 4 +--R (256a x + 256a x + 32a x)y(x) +--R + +--R 6 4 2 3 +--R (- 128x - 320x - 192x - 16)y(x) +--R + +--R 5 3 2 +--R (128a x + 128a x + 16a x)y(x) +--R + +--R 6 4 2 +--R (- 64x - 112x - 48x - 2)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) + 1 +--R + +--R 3 4 3 2 3 +--R (- 128x - 64x)y(x) + (- 128x - 64x)y(x) - 16x +--R + +--R - 8x +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 4 2 4 4 2 2 +--R (128x + 128x + 16)y(x) + (128x + 128x + 16)y(x) +--R + +--R 4 2 +--R 16x + 16x + 2 +--R * +--R +------+ +--R | 2 +--R log(\|x + 1 - x) +--R + +--R 3 6 4 2 5 +--R (- 128x - 64x)y(x) + (256a x + 128a x )y(x) +--R + +--R 5 3 4 4 2 3 +--R (- 128x - 320x - 112x)y(x) + (256a x + 128a x )y(x) +--R + +--R 5 3 2 4 2 +--R (- 128x - 192x - 48x)y(x) + (32a x + 16a x )y(x) +--R + +--R 5 3 +--R - 16x - 16x - 2x +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 4 2 6 +--R (128x + 128x + 16)y(x) +--R + +--R 5 3 5 +--R (- 256a x - 256a x - 32a x)y(x) +--R + +--R 6 4 2 4 +--R (128x + 384x + 256x + 24)y(x) +--R + +--R 5 3 3 +--R (- 256a x - 256a x - 32a x)y(x) +--R + +--R 6 4 2 2 +--R (128x + 256x + 128x + 8)y(x) +--R + +--R 5 3 6 4 2 +--R (- 32a x - 32a x - 4a x)y(x) + 16x + 24x + 8x +--R * +--R +---------+ +--R | 2 +--R log(\|y(x) + 1 - y(x)) +--R + +--R +------+ +--R 3 3 3 | 2 +--R ((64x + 32x)y(x) + (32x + 16x)y(x))\|x + 1 +--R + +--R 4 2 3 4 2 +--R (- 64x - 64x - 8)y(x) + (- 32x - 32x - 4)y(x) +--R * +--R +------+ 2 +--R | 2 +--R log(\|x + 1 - x) +--R + +--R 3 5 4 2 4 +--R (128x + 64x)y(x) + (- 256a x - 128a x )y(x) +--R + +--R 5 3 3 +--R (128x + 256x + 80x)y(x) +--R + +--R 4 2 2 5 3 +--R (- 128a x - 64a x )y(x) + (64x + 80x + 16x)y(x) +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 4 2 5 +--R (- 128x - 128x - 16)y(x) +--R + +--R 5 3 4 +--R (256a x + 256a x + 32a x)y(x) +--R + +--R 6 4 2 3 +--R (- 128x - 320x - 192x - 16)y(x) +--R + +--R 5 3 2 +--R (128a x + 128a x + 16a x)y(x) +--R + +--R 6 4 2 +--R (- 64x - 112x - 48x - 2)y(x) +--R * +--R +------+ +--R | 2 +--R log(\|x + 1 - x) +--R + +--R 3 7 4 2 6 +--R (64x + 32x)y(x) + (- 256a x - 128a x )y(x) +--R + +--R 2 5 2 3 5 +--R ((256a + 128)x + (128a + 224)x + 64x)y(x) +--R + +--R 6 4 2 4 +--R (- 256a x - 512a x - 160a x )y(x) +--R + +--R 7 2 5 2 3 3 +--R (64x + (128a + 224)x + (64a + 448)x + 160x)y(x) +--R + +--R 6 4 2 2 +--R (- 128a x - 160a x - 32a x )y(x) +--R + +--R 7 5 3 +--R (32x + 64x + 160x + 66x)y(x) +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 4 2 7 5 3 6 +--R (- 64x - 64x - 8)y(x) + (256a x + 256a x + 32a x)y(x) +--R + +--R 2 6 2 4 2 2 +--R (- 256a - 128)x + (- 256a - 288)x + (- 32a - 160)x +--R + +--R - 12 +--R * +--R 5 +--R y(x) +--R + +--R 7 5 3 4 +--R (256a x + 640a x + 384a x + 32a x)y(x) +--R + +--R 8 2 6 2 4 +--R - 64x + (- 128a - 256)x + (- 128a - 552)x +--R + +--R 2 2 +--R (- 16a - 360)x - 36 +--R * +--R 3 +--R y(x) +--R + +--R 7 5 3 2 +--R (128a x + 224a x + 96a x + 4a x)y(x) +--R + +--R 8 6 4 2 +--R (- 32x - 80x - 188x - 140x - 16)y(x) +--R * +--R +---------+ +--R | 2 +--R \|y(x) + 1 +--R + +--R 3 4 3 2 3 +--R ((- 64x - 32x)y(x) + (- 64x - 32x)y(x) - 8x - 4x) +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 4 2 4 4 2 2 4 2 +--R (64x + 64x + 8)y(x) + (64x + 64x + 8)y(x) + 8x + 8x +--R + +--R 1 +--R * +--R +------+ 2 +--R | 2 +--R log(\|x + 1 - x) +--R + +--R 3 6 4 2 5 +--R (- 128x - 64x)y(x) + (256a x + 128a x )y(x) +--R + +--R 5 3 4 4 2 3 +--R (- 128x - 320x - 112x)y(x) + (256a x + 128a x )y(x) +--R + +--R 5 3 2 4 2 +--R (- 128x - 192x - 48x)y(x) + (32a x + 16a x )y(x) +--R + +--R 5 3 +--R - 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x - 1216a x - 192a x)y(x) +--R + +--R 7 5 3 5 +--R (- 2048a x - 4096a x - 2432a x - 384a x)y(x) +--R + +--R 7 5 3 3 +--R (- 1216a x - 2432a x - 1444a x - 228a x)y(x) +--R + +--R 7 5 3 +--R (- 192a x - 384a x - 228a x - 36a x)y(x) +--R * +--R +---------+ +--R | 2 +--R log(\|y(x) + 1 - y(x)) +--R + +--R 7 5 3 7 +--R (- 2048a x - 3072a x - 1152a x - 64a x)y(x) +--R + +--R 2 8 2 6 2 4 2 2 6 +--R (2048a x + 3072a x + 1152a x + 64a x )y(x) +--R + +--R 7 5 3 5 +--R (- 4096a x - 6144a x - 2304a x - 128a x)y(x) +--R + +--R 2 8 2 6 2 4 2 2 4 +--R (3072a x + 4608a x + 1728a x + 96a x )y(x) +--R + +--R 7 5 3 3 +--R (- 2432a x - 3648a x - 1368a x - 76a x)y(x) +--R + +--R 2 8 2 6 2 4 2 2 2 +--R (1152a x + 1728a x + 648a x + 36a x )y(x) +--R + +--R 7 5 3 2 8 2 6 +--R (- 384a x - 576a x - 216a x - 12a x)y(x) + 64a x + 96a x +--R + +--R 2 4 2 2 +--R 36a x + 2a x +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 8 6 4 2 7 +--R (2048a x + 4096a x + 2432a x + 384a x )y(x) +--R + +--R 2 9 2 7 2 5 2 3 6 +--R (- 2048a x - 4096a x - 2432a x - 384a x )y(x) +--R + +--R 8 6 4 2 5 +--R (4096a x + 8192a x + 4864a x + 768a x )y(x) +--R + +--R 2 9 2 7 2 5 2 3 4 +--R (- 3072a x - 6144a x - 3648a x - 576a x )y(x) +--R + +--R 8 6 4 2 3 +--R (2432a x + 4864a x + 2888a x + 456a x )y(x) +--R + +--R 2 9 2 7 2 5 2 3 2 +--R (- 1152a x - 2304a x - 1368a x - 216a x )y(x) +--R + +--R 8 6 4 2 2 9 2 7 +--R (384a x + 768a x + 456a x + 72a x )y(x) - 64a x - 128a x +--R + +--R 2 5 2 3 +--R - 76a x - 12a x +--R * +--R +---------+ +--R | 2 +--R \|y(x) + 1 +--R + +--R 7 5 3 8 +--R (2048a x + 3072a x + 1152a x + 64a x)y(x) +--R + +--R 2 8 2 6 2 4 2 2 7 +--R (- 2048a x - 3072a x - 1152a x - 64a x )y(x) +--R + +--R 7 5 3 6 +--R (5120a x + 7680a x + 2880a x + 160a x)y(x) +--R + +--R 2 8 2 6 2 4 2 2 5 +--R (- 4096a x - 6144a x - 2304a x - 128a x )y(x) +--R + +--R 7 5 3 4 +--R (4224a x + 6336a x + 2376a x + 132a x)y(x) +--R + +--R 2 8 2 6 2 4 2 2 3 +--R (- 2432a x - 3648a x - 1368a x - 76a x )y(x) +--R + +--R 7 5 3 2 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1536a x - 2304a x - 864a x - 48a)y(x) +--R + +--R 6 4 2 2 6 4 +--R (- 576a x - 864a x - 324a x - 18a)y(x) - 32a x - 48a x +--R + +--R 2 +--R - 18a x - a +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 7 5 3 6 +--R (1024a x + 2048a x + 1216a x + 192a x)y(x) +--R + +--R 7 5 3 4 +--R (1536a x + 3072a x + 1824a x + 288a x)y(x) +--R + +--R 7 5 3 2 7 5 +--R (576a x + 1152a x + 684a x + 108a x)y(x) + 32a x + 64a x +--R + +--R 3 +--R 38a x + 6a x +--R * +--R +------+ +--R | 2 +--R log(\|x + 1 - x) +--R + +--R 6 4 2 8 +--R (- 1024a x - 1536a x - 576a x - 32a)y(x) +--R + +--R 2 7 2 5 2 3 2 7 +--R (4096a x + 6144a x + 2304a x + 128a x)y(x) +--R + +--R 8 7 6 5 4 3 +--R - 3072a x - 2048x - 8192a x - 4096x - 6720a x - 2432x +--R + +--R 2 +--R - 1728a x - 384x - 64a +--R * +--R 6 +--R y(x) +--R + +--R 2 7 2 5 2 3 2 5 +--R (6144a x + 9216a x + 3456a x + 192a x)y(x) +--R + +--R 8 7 6 5 4 3 +--R - 4608a x - 3072x - 10432a x - 6144x - 7296a x - 3648x +--R + +--R 2 +--R - 1548a x - 576x - 38a +--R * +--R 4 +--R y(x) +--R + +--R 2 7 2 5 2 3 2 3 +--R (2304a x + 3456a x + 1296a x + 72a x)y(x) +--R + +--R 8 7 6 5 4 3 +--R - 1728a x - 1152x - 3648a x - 2304x - 2340a x - 1368x +--R + +--R 2 +--R - 432a x - 216x - 6a +--R * +--R 2 +--R y(x) +--R + +--R 2 7 2 5 2 3 2 8 7 6 +--R (128a x + 192a x + 72a x + 4a x)y(x) - 96a x - 64x - 192a x +--R + +--R 5 4 3 2 +--R - 128x - 114a x - 76x - 18a x - 12x +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 7 5 3 8 +--R (1024a x + 2048a x + 1216a x + 192a x)y(x) +--R + +--R 2 8 2 6 2 4 2 2 7 +--R (- 4096a x - 8192a x - 4864a x - 768a x )y(x) +--R + +--R 9 8 7 6 5 4 +--R 3072a x + 2048x + 9728a x + 5120x + 10432a x + 4224x +--R + +--R 3 2 +--R 4256a x + 1216x + 480a x + 64 +--R * +--R 6 +--R y(x) +--R + +--R 2 8 2 6 2 4 2 2 5 +--R (- 6144a x - 12288a x - 7296a x - 1152a x )y(x) +--R + +--R 9 8 7 6 5 4 +--R 4608a x + 3072x + 12736a x + 7680x + 11936a x + 6336x +--R + +--R 3 2 +--R 4180a x + 1824x + 372a x + 96 +--R * +--R 4 +--R y(x) +--R + +--R 2 8 2 6 2 4 2 2 3 +--R (- 2304a x - 4608a x - 2736a x - 432a x )y(x) +--R + +--R 9 8 7 6 5 4 +--R 1728a x + 1152x + 4512a x + 2880x + 3948a x + 2376x +--R + +--R 3 2 +--R 1254a x + 684x + 90a x + 36 +--R * +--R 2 +--R y(x) +--R + +--R 2 8 2 6 2 4 2 2 9 8 +--R (- 128a x - 256a x - 152a x - 24a x )y(x) + 96a x + 64x +--R + +--R 7 6 5 4 3 2 +--R 240a x + 160x + 198a x + 132x + 57a x + 38x + 3a x + 2 +--R * +--R +---------+ +--R | 2 +--R \|y(x) + 1 +--R + +--R 6 4 2 7 +--R (1024a x + 1536a x + 576a x + 32a)y(x) +--R + +--R 6 4 2 5 +--R (2048a x + 3072a x + 1152a x + 64a)y(x) +--R + +--R 6 4 2 3 +--R (1216a x + 1824a x + 684a x + 38a)y(x) +--R + +--R 6 4 2 +--R (192a x + 288a x + 108a x + 6a)y(x) +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 7 5 3 7 +--R (- 1024a x - 2048a x - 1216a x - 192a x)y(x) +--R + +--R 7 5 3 5 +--R (- 2048a x - 4096a x - 2432a x - 384a x)y(x) +--R + +--R 7 5 3 3 +--R (- 1216a x - 2432a x - 1444a x - 228a x)y(x) +--R + +--R 7 5 3 +--R (- 192a x - 384a x - 228a x - 36a x)y(x) +--R * +--R +------+ +--R | 2 +--R log(\|x + 1 - x) +--R + +--R 6 4 2 9 +--R (1024a x + 1536a x + 576a x + 32a)y(x) +--R + +--R 2 7 2 5 2 3 2 8 +--R (- 4096a x - 6144a x - 2304a x - 128a x)y(x) +--R + +--R 8 7 6 5 4 3 +--R 3072a x + 2048x + 8704a x + 4096x + 7488a x + 2432x +--R + +--R 2 +--R 2016a x + 384x + 80a +--R * +--R 7 +--R y(x) +--R + +--R 2 7 2 5 2 3 2 6 +--R (- 8192a x - 12288a x - 4608a x - 256a x)y(x) +--R + +--R 8 7 6 5 4 3 +--R 6144a x + 4096x + 14400a x + 8192x + 10464a x + 4864x +--R + +--R 2 +--R 2340a x + 768x + 66a +--R * +--R 5 +--R y(x) +--R + +--R 2 7 2 5 2 3 2 4 +--R (- 4864a x - 7296a x - 2736a x - 152a x)y(x) +--R + +--R 8 7 6 5 4 3 +--R 3648a x + 2432x + 7904a x + 4864x + 5244a x + 2888x +--R + +--R 2 +--R 1026a x + 456x + 19a +--R * +--R 3 +--R y(x) +--R + +--R 2 7 2 5 2 3 2 2 +--R (- 768a x - 1152a x - 432a x - 24a x)y(x) +--R + +--R 8 7 6 5 4 3 2 +--R 576a x + 384x + 1184a x + 768x + 732a x + 456x + 126a x +--R + +--R 72x + a +--R * +--R y(x) +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 7 5 3 9 +--R (- 1024a x - 2048a x - 1216a x - 192a x)y(x) +--R + +--R 2 8 2 6 2 4 2 2 8 +--R (4096a x + 8192a x + 4864a x + 768a x )y(x) +--R + +--R 9 8 7 6 5 4 +--R - 3072a x - 2048x - 10240a x - 5120x - 11456a x - 4224x +--R + +--R 3 2 +--R - 4864a x - 1216x - 576a x - 64 +--R * +--R 7 +--R y(x) +--R + +--R 2 8 2 6 2 4 2 2 6 +--R (8192a x + 16384a x + 9728a x + 1536a x )y(x) +--R + +--R 9 8 7 6 5 4 +--R - 6144a x - 4096x - 17472a x - 10240x - 16896a x - 8448x +--R + +--R 3 2 +--R - 6156a x - 2432x - 588a x - 128 +--R * +--R 5 +--R y(x) +--R + +--R 2 8 2 6 2 4 2 2 4 +--R (4864a x + 9728a x + 5776a x + 912a x )y(x) +--R + +--R 9 8 7 6 5 4 +--R - 3648a x - 2432x - 9728a x - 6080x - 8740a x - 5016x +--R + +--R 3 2 +--R - 2888a x - 1444x - 228a x - 76 +--R * +--R 3 +--R y(x) +--R + +--R 2 8 2 6 2 4 2 2 2 +--R (768a x + 1536a x + 912a x + 144a x )y(x) +--R + +--R 9 8 7 6 5 4 3 +--R - 576a x - 384x - 1472a x - 960x - 1252a x - 792x - 380a x +--R + +--R 2 +--R - 228x - 24a x - 12 +--R * +--R y(x) +--R / +--R 6 4 2 6 +--R (2048x + 3072x + 1152x + 64)y(x) +--R + +--R 6 4 2 4 +--R (3072x + 4608x + 1728x + 96)y(x) +--R + +--R 6 4 2 2 6 4 2 +--R (1152x + 1728x + 648x + 36)y(x) + 64x + 96x + 36x + 2 +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 7 5 3 6 +--R (- 2048x - 4096x - 2432x - 384x)y(x) +--R + +--R 7 5 3 4 +--R (- 3072x - 6144x - 3648x - 576x)y(x) +--R + +--R 7 5 3 2 7 5 3 +--R (- 1152x - 2304x - 1368x - 216x)y(x) - 64x - 128x - 76x - 12x +--R * +--R +---------+ +--R | 2 +--R \|y(x) + 1 +--R + +--R 6 4 2 7 +--R (- 2048x - 3072x - 1152x - 64)y(x) +--R + +--R 6 4 2 5 +--R (- 4096x - 6144x - 2304x - 128)y(x) +--R + +--R 6 4 2 3 +--R (- 2432x - 3648x - 1368x - 76)y(x) +--R + +--R 6 4 2 +--R (- 384x - 576x - 216x - 12)y(x) +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 7 5 3 7 +--R (2048x + 4096x + 2432x + 384x)y(x) +--R + +--R 7 5 3 5 +--R (4096x + 8192x + 4864x + 768x)y(x) +--R + +--R 7 5 3 3 7 5 3 +--R (2432x + 4864x + 2888x + 456x)y(x) + (384x + 768x + 456x + 72x)y(x) +--R Type: Expression Integer +--E 85 + +--S 86 of 120 +--Rode337 := (sqrt(y(x)**2+x**2)+x)*D(y(x),x)-y(x) +--R +--R +--R +----------+ +--R | 2 2 , +--R (85) (\|y(x) + x + x)y (x) - y(x) +--R +--R Type: Expression Integer +--E 86 + +--S 87 of 120 +--Rsolve(ode337,y,x) +--R +--R +--R (86) "failed" +--R Type: Union("failed",...) +--E 87 + +--S 88 of 120 +--Rode338 := (y(x)*sqrt(y(x)**2+x**2)+(y(x)**2-x**2)*sin(alpha)-_ +--R 2*x*y(x)*cos(alpha))*D(y(x),x)+x*sqrt(y(x)**2+x**2)+_ +--R 2*x*y(x)*sin(alpha)+(y(x)**2-x**2)*cos(alpha) +--R +--R +--R (87) +--R +----------+ +--R | 2 2 2 2 , +--R (y(x)\|y(x) + x + (y(x) - x )sin(alpha) - 2x y(x)cos(alpha))y (x) +--R +--R + +--R +----------+ +--R | 2 2 2 2 +--R x\|y(x) + x + 2x y(x)sin(alpha) + (y(x) - x )cos(alpha) +--R Type: Expression Integer +--E 88 + +--S 89 of 120 +--Rsolve(ode338,y,x) +--R +--R +--R (88) "failed" +--R Type: Union("failed",...) +--E 89 + +--S 90 of 120 +--Rode339 := (x*sqrt(x**2+y(x)**2+1)-y(x)*(x**2+y(x)**2))*D(y(x),x)-_ +--R y(x)*sqrt(x**2+y(x)**2+1)-x*(x**2+y(x)**2) +--R +--R +--R (89) +--R +--------------+ +--------------+ +--R | 2 2 3 2 , | 2 2 +--R (x\|y(x) + x + 1 - y(x) - x y(x))y (x) - y(x)\|y(x) + x + 1 +--R +--R + +--R 2 3 +--R - x y(x) - x +--R Type: Expression Integer +--E 90 + +--S 91 of 120 +--Rsolve(ode339,y,x) +--R +--R +--R (90) "failed" +--R Type: Union("failed",...) +--E 91 + +--S 92 of 120 +--Rode340 := (e1*(x+a)/((x+a)**2+y(x)**2)**(3/2)+e2*(x-a)/_ +--R ((x-a)**2+y(x)**2)**(3/2))*D(y(x),x)-y(x)*_ +--R (e1/((x+a)**2+y(x)**2)**(3/2)+e2/((x-a)**2+y(x)**2)**(3/2)) +--R +--R +--R (91) +--R 2 3 2 2 3 +--R ((e2 x - a e2)y(x) + e2 x + a e2 x - a e2 x - a e2) +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|y(x) + x + 2a x + a +--R + +--R 2 3 2 2 3 +--R ((e1 x + a e1)y(x) + e1 x - a e1 x - a e1 x + a e1) +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|y(x) + x - 2a x + a +--R * +--R , +--R y (x) +--R +--R + +--R +----------------------+ +--R 3 2 2 | 2 2 2 +--R (- e2 y(x) + (- e2 x - 2a e2 x - a e2)y(x))\|y(x) + x + 2a x + a +--R + +--R +----------------------+ +--R 3 2 2 | 2 2 2 +--R (- e1 y(x) + (- e1 x + 2a e1 x - a e1)y(x))\|y(x) + x - 2a x + a +--R / +--R +----------------------+ +--R 4 2 2 2 4 2 2 4 | 2 2 2 +--R (y(x) + (2x + 2a )y(x) + x - 2a x + a )\|y(x) + x - 2a x + a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|y(x) + x + 2a x + a +--R Type: Expression Integer +--E 92 + +--S 93 of 120 +--Rsolve(ode340,y,x) +--R +--R +--R (92) "failed" +--R Type: Union("failed",...) +--E 93 + +--S 94 of 120 +--Rode341 := (x*exp(y(x))+exp(x))*D(y(x),x)+exp(y(x))+y(x)*exp(x) +--R +--R +--R y(x) x , y(x) x +--R (93) (x %e + %e )y (x) + %e + y(x)%e +--R +--R Type: Expression Integer +--E 94 + +--S 95 of 120 +--Ryx:=solve(ode341,y,x) +--R +--R +--R y(x) x +--R (94) x %e + y(x)%e +--R Type: Union(Expression Integer,...) +--E 95 + +--S 96 of 120 +--Rode341expr := (x*exp(yx)+exp(x))*D(yx,x)+exp(yx)+yx*exp(x) +--R +--R +--R (95) +--R y(x) x +--R 2 y(x) x , y(x) x x %e + y(x)%e +--R ((x %e + x %e )y (x) + x %e + x y(x)%e + 1)%e +--R +--R + +--R x y(x) x 2 , x y(x) x 2 +--R (x %e %e + (%e ) )y (x) + (x + 1)%e %e + 2y(x)(%e ) +--R +--R Type: Expression Integer +--E 96 + +--S 97 of 120 +--Rode342 := x*(3*exp(x*y(x))+2*exp(-x*y(x)))*(x*D(y(x),x)+y(x))+1 +--R +--R +--R (96) +--R 2 x y(x) 2 - x y(x) , x y(x) - x y(x) +--R (3x %e + 2x %e )y (x) + 3x y(x)%e + 2x y(x)%e + 1 +--R +--R Type: Expression Integer +--E 97 + +--S 98 of 120 +--Ryx:=solve(ode342,y,x) +--R +--R +--R x y(x) 2 x y(x) +--R 3(%e ) + log(x)%e - 2 +--R (97) --------------------------------- +--R x y(x) +--R %e +--R Type: Union(Expression Integer,...) +--E 98 + +--S 99 of 120 +--Rode342expr := x*(3*exp(x*yx)+2*exp(-x*yx))*(x*D(yx,x)+yx)+1 +--R +--R +--R (98) +--R 3 x y(x) 2 3 , 2 x y(x) 2 +--R (9x (%e ) + 6x )y (x) + (9x y(x) + 9x)(%e ) +--R +--R + +--R x y(x) 2 +--R (3x log(x) + 3x)%e + 6x y(x) - 6x +--R * +--R x y(x) 2 x y(x) +--R 3x (%e ) + x log(x)%e - 2x +--R -------------------------------------- +--R x y(x) +--R %e +--R %e +--R + +--R 3 x y(x) 2 3 , 2 x y(x) 2 +--R (6x (%e ) + 4x )y (x) + (6x y(x) + 6x)(%e ) +--R +--R + +--R x y(x) 2 +--R (2x log(x) + 2x)%e + 4x y(x) - 4x +--R * +--R x y(x) 2 x y(x) +--R - 3x (%e ) - x log(x)%e + 2x +--R ---------------------------------------- +--R x y(x) +--R %e +--R %e +--R + +--R x y(x) +--R %e +--R / +--R x y(x) +--R %e +--R Type: Expression Integer +--E 99 + +--S 100 of 120 +--Rode343 := (log(y(x))+x)*D(y(x),x)-1 +--R +--R +--R , +--R (99) (log(y(x)) + x)y (x) - 1 +--R +--R Type: Expression Integer +--E 100 + +--S 101 of 120 +--Ryx:=solve(ode343,y,x) +--R +--R +--R - y(x) - y(x) +--R (100) - %e log(y(x)) - x %e + Ei(- y(x)) +--R Type: Union(Expression Integer,...) +--E 101 + +--S 102 of 120 +--Rode343expr := (log(yx)+x)*D(yx,x)-1 +--R +--R +--R (101) +--R - y(x) - y(x) , - y(x) +--R ((%e log(y(x)) + x %e )y (x) - %e ) +--R +--R * +--R - y(x) - y(x) +--R log(- %e log(y(x)) - x %e + Ei(- y(x))) +--R + +--R - y(x) 2 - y(x) , - y(x) +--R (x %e log(y(x)) + x %e )y (x) - x %e - 1 +--R +--R Type: Expression Integer +--E 102 + +--S 103 of 120 +--Rode344 := (log(y(x))+2*x-1)*D(y(x),x)-2*y(x) +--R +--R +--R , +--R (102) (log(y(x)) + 2x - 1)y (x) - 2y(x) +--R +--R Type: Expression Integer +--E 103 + +--S 104 of 120 +--Ryx:=solve(ode344,y,x) +--R +--R +--R - log(y(x)) - 2x +--R (103) ---------------- +--R y(x) +--R Type: Union(Expression Integer,...) +--E 104 + +--S 105 of 120 +--Rode344expr := (log(yx)+2*x-1)*D(yx,x)-2*yx +--R +--R +--R (104) +--R , - log(y(x)) - 2x +--R ((log(y(x)) + 2x - 1)y (x) - 2y(x))log(----------------) +--R y(x) +--R + +--R 2 , +--R ((2x - 1)log(y(x)) + 4x - 4x + 1)y (x) + 2y(x)log(y(x)) + 2y(x) +--R +--R / +--R 2 +--R y(x) +--R Type: Expression Integer +--E 105 + +--S 106 of 120 +--Rode345 := x*(2*x**2*y(x)*log(y(x))+1)*D(y(x),x)-2*y(x) +--R +--R +--R 3 , +--R (105) (2x y(x)log(y(x)) + x)y (x) - 2y(x) +--R +--R Type: Expression Integer +--E 106 + +--S 107 of 120 +--Ryx:=solve(ode345,y,x) +--R +--R +--R 2 2 2 2 +--R 2x y(x) log(y(x)) - x y(x) + 2y(x) +--R (106) ----------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression Integer,...) +--E 107 + +--S 108 of 120 +--Rode345expr := x*(2*x**2*yx*log(yx)+1)*D(yx,x)-2*yx +--R +--R +--R (107) +--R 5 3 2 5 3 3 2 3 2 +--R 4x y(x) log(y(x)) + (- 2x y(x) + 6x y(x) )log(y(x)) - x y(x) +--R + +--R 2x y(x) +--R * +--R , +--R y (x) +--R +--R + +--R 2 3 2 3 2 +--R - 4x y(x) log(y(x)) + 2x y(x) - 4y(x) +--R * +--R 2 2 2 2 +--R 2x y(x) log(y(x)) - x y(x) + 2y(x) +--R log(-----------------------------------) +--R 2 +--R 2x +--R + +--R 3 , 2 2 2 2 +--R (2x y(x)log(y(x)) + x)y (x) - 2x y(x) log(y(x)) + x y(x) - 4y(x) +--R +--R / +--R 2 +--R x +--R Type: Expression Integer +--E 108 + +--S 109 of 120 +--Rode346 := x*(y(x)*log(x*y(x))+y(x)-a*x)*D(y(x),x)-_ +--R y(x)*(a*x*log(x*y(x))-y(x)+a*x) +--R +--R +--R (108) +--R 2 , 2 +--R (x y(x)log(x y(x)) + x y(x) - a x )y (x) - a x y(x)log(x y(x)) + y(x) +--R +--R + +--R - a x y(x) +--R Type: Expression Integer +--E 109 + +--S 110 of 120 +--Rsolve(ode346,y,x) +--R +--R +--R (109) "failed" +--R Type: Union("failed",...) +--E 110 + +--S 111 of 120 +--Rode347 := D(y(x),x)*(1+sin(x))*sin(y(x))+cos(x)*(cos(y(x))-1) +--R +--R +--R , +--R (110) (sin(x) + 1)sin(y(x))y (x) + cos(x)cos(y(x)) - cos(x) +--R +--R Type: Expression Integer +--E 111 + +--S 112 of 120 +--Ryx:=solve(ode347,y,x) +--R +--R +--R (111) +--R 2 2 2 +--R (- 4cos(x) - 8cos(x) - 4)sin(x) + (- 8cos(x) - 16cos(x) - 8)sin(x) +--R + +--R 2 +--R - 4cos(x) - 8cos(x) - 4 +--R * +--R cos(y(x)) +--R + +--R 5 4 2 3 +--R - sin(x) + (- 4cos(x) - 4)sin(x) + (- 6cos(x) - 12cos(x) - 6)sin(x) +--R + +--R 3 2 2 +--R (- 4cos(x) - 12cos(x) - 12cos(x) - 4)sin(x) +--R + +--R 4 3 2 +--R (- cos(x) - 4cos(x) - 6cos(x) - 4cos(x) - 1)sin(x) +--R / +--R 5 4 2 3 +--R sin(x) + (4cos(x) + 5)sin(x) + (6cos(x) + 16cos(x) + 10)sin(x) +--R + +--R 3 2 2 +--R (4cos(x) + 18cos(x) + 24cos(x) + 10)sin(x) +--R + +--R 4 3 2 4 +--R (cos(x) + 8cos(x) + 18cos(x) + 16cos(x) + 5)sin(x) + cos(x) +--R + +--R 3 2 +--R 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R Type: Union(Expression Integer,...) +--E 112 + +--S 113 of 120 +--Rode347expr := D(yx,x)*(1+sin(x))*sin(yx)+cos(x)*(cos(yx)-1) +--R +--R +--R (112) +--R 2 4 +--R (- 4cos(x) - 8cos(x) - 4)sin(x) +--R + +--R 3 2 3 +--R (- 4cos(x) - 24cos(x) - 36cos(x) - 16)sin(x) +--R + +--R 3 2 2 +--R (- 12cos(x) - 48cos(x) - 60cos(x) - 24)sin(x) +--R + +--R 3 2 3 +--R (- 12cos(x) - 40cos(x) - 44cos(x) - 16)sin(x) - 4cos(x) +--R + +--R 2 +--R - 12cos(x) - 12cos(x) - 4 +--R * +--R , +--R sin(y(x))y (x) +--R +--R + +--R 5 2 4 +--R (- 8cos(x) - 8)sin(x) + (8cos(x) - 8cos(x) - 16)sin(x) +--R + +--R 3 3 +--R (- 12cos(x) + 12cos(x))sin(x) +--R + +--R 4 3 2 2 +--R (4cos(x) - 28cos(x) - 44cos(x) + 4cos(x) + 16)sin(x) +--R + +--R 4 3 2 +--R (8cos(x) - 20cos(x) - 56cos(x) - 20cos(x) + 8)sin(x) +--R + +--R 4 3 2 +--R 4cos(x) - 4cos(x) - 20cos(x) - 12cos(x) +--R * +--R cos(y(x)) +--R + +--R 5 2 4 +--R cos(x)sin(x) + (5cos(x) + 5cos(x))sin(x) +--R + +--R 3 2 3 +--R (10cos(x) + 20cos(x) + 10cos(x))sin(x) +--R + +--R 4 3 2 2 +--R (10cos(x) + 30cos(x) + 30cos(x) + 10cos(x))sin(x) +--R + +--R 5 4 3 2 +--R (5cos(x) + 20cos(x) + 30cos(x) + 20cos(x) + 5cos(x))sin(x) +--R + +--R 6 5 4 3 2 +--R cos(x) + 5cos(x) + 10cos(x) + 10cos(x) + 5cos(x) + cos(x) +--R * +--R sin +--R 2 2 +--R (4cos(x) + 8cos(x) + 4)sin(x) +--R + +--R 2 2 +--R (8cos(x) + 16cos(x) + 8)sin(x) + 4cos(x) + 8cos(x) + 4 +--R * +--R cos(y(x)) +--R + +--R 5 4 +--R sin(x) + (4cos(x) + 4)sin(x) +--R + +--R 2 3 +--R (6cos(x) + 12cos(x) + 6)sin(x) +--R + +--R 3 2 2 +--R (4cos(x) + 12cos(x) + 12cos(x) + 4)sin(x) +--R + +--R 4 3 2 +--R (cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1)sin(x) +--R / +--R 5 4 +--R sin(x) + (4cos(x) + 5)sin(x) +--R + +--R 2 3 +--R (6cos(x) + 16cos(x) + 10)sin(x) +--R + +--R 3 2 2 +--R (4cos(x) + 18cos(x) + 24cos(x) + 10)sin(x) +--R + +--R 4 3 2 4 +--R (cos(x) + 8cos(x) + 18cos(x) + 16cos(x) + 5)sin(x) + cos(x) +--R + +--R 3 2 +--R 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 6 2 5 +--R cos(x)sin(x) + (5cos(x) + 6cos(x))sin(x) +--R + +--R 3 2 4 +--R (10cos(x) + 25cos(x) + 15cos(x))sin(x) +--R + +--R 4 3 2 3 +--R (10cos(x) + 40cos(x) + 50cos(x) + 20cos(x))sin(x) +--R + +--R 5 4 3 2 2 +--R (5cos(x) + 30cos(x) + 60cos(x) + 50cos(x) + 15cos(x))sin(x) +--R + +--R 6 5 4 3 2 +--R (cos(x) + 10cos(x) + 30cos(x) + 40cos(x) + 25cos(x) + 6cos(x)) +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R cos(x) + 5cos(x) + 10cos(x) + 10cos(x) + 5cos(x) + cos(x) +--R * +--R cos +--R 2 2 +--R (4cos(x) + 8cos(x) + 4)sin(x) +--R + +--R 2 2 +--R (8cos(x) + 16cos(x) + 8)sin(x) + 4cos(x) + 8cos(x) + 4 +--R * +--R cos(y(x)) +--R + +--R 5 4 +--R sin(x) + (4cos(x) + 4)sin(x) +--R + +--R 2 3 +--R (6cos(x) + 12cos(x) + 6)sin(x) +--R + +--R 3 2 2 +--R (4cos(x) + 12cos(x) + 12cos(x) + 4)sin(x) +--R + +--R 4 3 2 +--R (cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1)sin(x) +--R / +--R 5 4 +--R sin(x) + (4cos(x) + 5)sin(x) +--R + +--R 2 3 +--R (6cos(x) + 16cos(x) + 10)sin(x) +--R + +--R 3 2 2 +--R (4cos(x) + 18cos(x) + 24cos(x) + 10)sin(x) +--R + +--R 4 3 2 4 +--R (cos(x) + 8cos(x) + 18cos(x) + 16cos(x) + 5)sin(x) + cos(x) +--R + +--R 3 2 +--R 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R + +--R 6 2 5 +--R - cos(x)sin(x) + (- 5cos(x) - 6cos(x))sin(x) +--R + +--R 3 2 4 +--R (- 10cos(x) - 25cos(x) - 15cos(x))sin(x) +--R + +--R 4 3 2 3 +--R (- 10cos(x) - 40cos(x) - 50cos(x) - 20cos(x))sin(x) +--R + +--R 5 4 3 2 2 +--R (- 5cos(x) - 30cos(x) - 60cos(x) - 50cos(x) - 15cos(x))sin(x) +--R + +--R 6 5 4 3 2 +--R (- cos(x) - 10cos(x) - 30cos(x) - 40cos(x) - 25cos(x) - 6cos(x)) +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - cos(x) - 5cos(x) - 10cos(x) - 10cos(x) - 5cos(x) - cos(x) +--R / +--R 6 5 2 4 +--R sin(x) + (5cos(x) + 6)sin(x) + (10cos(x) + 25cos(x) + 15)sin(x) +--R + +--R 3 2 3 +--R (10cos(x) + 40cos(x) + 50cos(x) + 20)sin(x) +--R + +--R 4 3 2 2 +--R (5cos(x) + 30cos(x) + 60cos(x) + 50cos(x) + 15)sin(x) +--R + +--R 5 4 3 2 +--R (cos(x) + 10cos(x) + 30cos(x) + 40cos(x) + 25cos(x) + 6)sin(x) +--R + +--R 5 4 3 2 +--R cos(x) + 5cos(x) + 10cos(x) + 10cos(x) + 5cos(x) + 1 +--R Type: Expression Integer +--E 113 + +--S 114 of 120 +--Rode348 := (x*cos(y(x))+sin(x))*D(y(x),x)+y(x)*cos(x)+sin(y(x)) +--R +--R +--R , +--R (113) (x cos(y(x)) + sin(x))y (x) + sin(y(x)) + y(x)cos(x) +--R +--R Type: Expression Integer +--E 114 + +--S 115 of 120 +--Ryx:=solve(ode348,y,x) +--R +--R +--R (114) x sin(y(x)) + y(x)sin(x) +--R Type: Union(Expression Integer,...) +--E 115 + +--S 116 of 120 +--Rode348expr := (x*cos(yx)+sin(x))*D(yx,x)+yx*cos(x)+sin(yx) +--R +--R +--R (115) +--R sin(x sin(y(x)) + y(x)sin(x)) +--R + +--R 2 , +--R ((x cos(y(x)) + x sin(x))y (x) + x sin(y(x)) + x y(x)cos(x)) +--R +--R * +--R cos(x sin(y(x)) + y(x)sin(x)) +--R + +--R 2 , +--R (x sin(x)cos(y(x)) + sin(x) )y (x) + (sin(x) + x cos(x))sin(y(x)) +--R +--R + +--R 2y(x)cos(x)sin(x) +--R Type: Expression Integer +--E 116 + +--S 117 of 120 +--Rode349 := x*D(y(x),x)*cot(y(x)/x)+2*x*sin(y(x)/x)-y(x)*cot(y(x)/x) +--R +--R +--R y(x) , y(x) y(x) +--R (116) x cot(----)y (x) + 2x sin(----) - y(x)cot(----) +--R x x x +--R Type: Expression Integer +--E 117 + +--S 118 of 120 +--Rsolve(ode349,y,x) +--R +--R +--R (117) "failed" +--R Type: Union("failed",...) +--E 118 + +--S 119 of 120 +--Rode350 := D(y(x),x)*cos(y(x))-cos(x)*sin(y(x))**2-sin(y(x)) +--R +--R +--R , 2 +--R (118) cos(y(x))y (x) - cos(x)sin(y(x)) - sin(y(x)) +--R +--R Type: Expression Integer +--E 119 + +--S 120 of 120 +--Rsolve(ode350,y,x) +--R +--R +--R (119) "failed" +--R Type: Union("failed",...) +--E 120 + + +)spool +)lisp (bye) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} {\bf http://www.cs.uwaterloo.ca/$\tilde{}$ecterrab/odetools.html} +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/kamke6.input.pdf b/src/axiom-website/CATS/kamke6.input.pdf new file 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S. Cheb-Terrab\cite{1}. They have been rewritten using Axiom +syntax. Where possible we show that the particular solution actually +satisfies the original ordinary differential equation. + +Note that after a certain point Axiom can no longer generate useful +results. The failures fall into several cases which have been included +in other regression test files. +\end{abstract} +\eject +\tableofcontents +\eject +\section{Generated results} +<<*>>= +)spool kamke7.output +)set break resume +)set mes auto off +)clear all + +--S 1 of 97 +y:=operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 1 + +--S 2 of 97 +f:=operator 'f +--R +--R +--R (2) f +--R Type: BasicOperator +--E 2 + +--S 3 of 97 +g:=operator 'g +--R +--R +--R (3) g +--R Type: BasicOperator +--E 3 + +--S 4 of 97 +h:=operator 'h +--R +--R +--R (4) h +--R Type: BasicOperator +--E 4 + +--S 5 of 97 +fa:=operator 'fa +--R +--R +--R (5) fa +--R Type: BasicOperator +--E 5 + +--S 6 of 97 +fb:=operator 'fb +--R +--R +--R (6) fb +--R Type: BasicOperator +--E 6 + +--S 7 of 97 +fc:=operator 'fc +--R +--R +--R (7) fc +--R Type: BasicOperator +--E 7 + +--S 8 of 97 +fd:=operator 'fd +--R +--R +--R (8) fd +--R Type: BasicOperator +--E 8 + +--S 9 of 97 +fe:=operator 'fe +--R +--R +--R (9) fe +--R Type: BasicOperator +--E 9 + +--S 10 of 97 +ff:=operator 'ff +--R +--R +--R (10) ff +--R Type: BasicOperator +--E 10 + +--S 11 of 97 +ode352 := D(y(x),x)*(cos(y(x))-sin(alpha)*sin(x))*cos(y(x))+(cos(x)-_ + sin(alpha)*sin(y(x)))*cos(x) +--R +--R +--R (11) +--R 2 , +--R (cos(y(x)) - sin(alpha)sin(x)cos(y(x)))y (x) - cos(x)sin(alpha)sin(y(x)) +--R +--R + +--R 2 +--R cos(x) +--R Type: Expression Integer +--E 11 + +--S 12 of 97 +yx:=solve(ode352,y,x) +--R +--R +--R (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x +--R (12) ------------------------------------------------------------------ +--R 2 +--R Type: Union(Expression Integer,...) +--E 12 + +--S 13 of 97 +ode352expr := D(yx,x)*(cos(yx)-sin(alpha)*sin(x))*cos(yx)+(cos(x)-_ + sin(alpha)*sin(yx))*cos(x) +--R +--R +--R (13) +--R - +--R 2cos(x)sin(alpha) +--R * +--R sin +--R (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) +--R + +--R y(x) + x +--R / +--R 2 +--R + +--R 2 2 , +--R (- sin(y(x)) + cos(y(x)) - 2sin(alpha)sin(x)cos(y(x)) + 1)y (x) +--R +--R + +--R 2 2 +--R - 2cos(x)sin(alpha)sin(y(x)) - sin(x) + cos(x) + 1 +--R * +--R (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x 2 +--R cos(------------------------------------------------------------------) +--R 2 +--R + +--R 2 2 +--R sin(alpha)sin(x)sin(y(x)) - sin(alpha)sin(x)cos(y(x)) +--R + +--R 2 2 +--R 2sin(alpha) sin(x) cos(y(x)) - sin(alpha)sin(x) +--R * +--R , +--R y (x) +--R +--R + +--R 2 3 +--R 2cos(x)sin(alpha) sin(x)sin(y(x)) + sin(alpha)sin(x) +--R + +--R 2 +--R (- cos(x) - 1)sin(alpha)sin(x) +--R * +--R (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x +--R cos(------------------------------------------------------------------) +--R 2 +--R + +--R 2 +--R 2cos(x) +--R / +--R 2 +--R Type: Expression Integer +--E 13 + +--S 14 of 97 +ode353 := x*D(y(x),x)*cos(y(x))+sin(y(x)) +--R +--R +--R , +--R (14) x cos(y(x))y (x) + sin(y(x)) +--R +--R Type: Expression Integer +--E 14 + +--S 15 of 97 +yx:=solve(ode353,y,x) +--R +--R +--R (15) x sin(y(x)) +--R Type: Union(Expression Integer,...) +--E 15 + +--S 16 of 97 +ode353expr := x*D(yx,x)*cos(yx)+sin(yx) +--R +--R +--R 2 , +--R (16) sin(x sin(y(x))) + (x cos(y(x))y (x) + x sin(y(x)))cos(x sin(y(x))) +--R +--R Type: Expression Integer +--E 16 + +--S 17 of 97 +ode354 := (x*sin(y(x))-1)*D(y(x),x)+cos(y(x)) +--R +--R +--R , +--R (17) (x sin(y(x)) - 1)y (x) + cos(y(x)) +--R +--R Type: Expression Integer +--E 17 + +--S 18 of 97 +yx:=solve(ode354,y,x) +--R +--R +--R - sin(y(x)) + x +--R (18) --------------- +--R cos(y(x)) +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 97 +ode354expr := (x*sin(yx)-1)*D(yx,x)+cos(yx) +--R +--R +--R (19) +--R 2 2 2 , +--R ((x sin(y(x)) - x sin(y(x)) + x cos(y(x)) )y (x) - x cos(y(x))) +--R +--R * +--R sin(y(x)) - x +--R sin(-------------) +--R cos(y(x)) +--R + +--R 2 sin(y(x)) - x +--R cos(y(x)) cos(-------------) +--R cos(y(x)) +--R + +--R 2 2 , +--R (sin(y(x)) - x sin(y(x)) + cos(y(x)) )y (x) - cos(y(x)) +--R +--R / +--R 2 +--R cos(y(x)) +--R Type: Expression Integer +--E 19 + +--S 20 of 97 +ode355 := (x*cos(y(x))+cos(x))*D(y(x),x)-y(x)*sin(x)+sin(y(x)) +--R +--R +--R , +--R (20) (x cos(y(x)) + cos(x))y (x) + sin(y(x)) - y(x)sin(x) +--R +--R Type: Expression Integer +--E 20 + +--S 21 of 97 +yx:=solve(ode355,y,x) +--R +--R +--R (21) x sin(y(x)) + y(x)cos(x) +--R Type: Union(Expression Integer,...) +--E 21 + +--S 22 of 97 +ode355expr := (x*cos(yx)+cos(x))*D(yx,x)-yx*sin(x)+sin(yx) +--R +--R +--R (22) +--R sin(x sin(y(x)) + y(x)cos(x)) +--R + +--R 2 , +--R ((x cos(y(x)) + x cos(x))y (x) + x sin(y(x)) - x y(x)sin(x)) +--R +--R * +--R cos(x sin(y(x)) + y(x)cos(x)) +--R + +--R 2 , +--R (x cos(x)cos(y(x)) + cos(x) )y (x) + (- x sin(x) + cos(x))sin(y(x)) +--R +--R + +--R - 2y(x)cos(x)sin(x) +--R Type: Expression Integer +--E 22 + +--S 23 of 97 +ode356 := (x**2*cos(y(x))+2*y(x)*sin(x))*D(y(x),x)+2*x*sin(y(x))+y(x)**2*cos(x) +--R +--R +--R 2 , 2 +--R (23) (x cos(y(x)) + 2y(x)sin(x))y (x) + 2x sin(y(x)) + y(x) cos(x) +--R +--R Type: Expression Integer +--E 23 + +--S 24 of 97 +yx:=solve(ode356,y,x) +--R +--R +--R 2 2 +--R (24) x sin(y(x)) + y(x) sin(x) +--R Type: Union(Expression Integer,...) +--E 24 + +--S 25 of 97 +ode356expr:=(x**2*cos(yx)+2*yx*sin(x))*D(yx,x)+2*x*sin(yx)+yx**2*cos(x) +--R +--R +--R (25) +--R 2 2 +--R 2x sin(x sin(y(x)) + y(x) sin(x)) +--R + +--R 4 2 , 3 2 2 +--R ((x cos(y(x)) + 2x y(x)sin(x))y (x) + 2x sin(y(x)) + x y(x) cos(x)) +--R +--R * +--R 2 2 +--R cos(x sin(y(x)) + y(x) sin(x)) +--R + +--R 4 2 2 +--R (2x sin(x)cos(y(x)) + 4x y(x)sin(x) )sin(y(x)) +--R + +--R 2 2 2 3 3 +--R 2x y(x) sin(x) cos(y(x)) + 4y(x) sin(x) +--R * +--R , +--R y (x) +--R +--R + +--R 3 4 2 +--R (4x sin(x) + x cos(x))sin(y(x)) +--R + +--R 2 2 2 2 4 2 +--R (4x y(x) sin(x) + 4x y(x) cos(x)sin(x))sin(y(x)) + 3y(x) cos(x)sin(x) +--R Type: Expression Integer +--E 25 + +--S 26 of 97 +ode358 := D(y(x),x)*sin(y(x))*cos(x)+cos(y(x))*sin(x) +--R +--R +--R , +--R (26) cos(x)sin(y(x))y (x) + sin(x)cos(y(x)) +--R +--R Type: Expression Integer +--E 26 + +--S 27 of 97 +yx:=solve(ode358,y,x) +--R +--R +--R (27) - cos(x)cos(y(x)) +--R Type: Union(Expression Integer,...) +--E 27 + +--S 28 of 97 +ode358expr := D(yx,x)*sin(yx)*cos(x)+cos(yx)*sin(x) +--R +--R +--R (28) +--R 2 , +--R (- cos(x) sin(y(x))y (x) - cos(x)sin(x)cos(y(x)))sin(cos(x)cos(y(x))) +--R +--R + +--R sin(x)cos(cos(x)cos(y(x))) +--R Type: Expression Integer +--E 28 + +--S 29 of 97 +ode361 := (x*sin(x*y(x))+cos(x+y(x))-sin(y(x)))*D(y(x),x)+_ + y(x)*sin(x*y(x))+cos(x+y(x))+cos(x) +--R +--R +--R (29) +--R , +--R (x sin(x y(x)) - sin(y(x)) + cos(y(x) + x))y (x) + y(x)sin(x y(x)) +--R +--R + +--R cos(y(x) + x) + cos(x) +--R Type: Expression Integer +--E 29 + +--S 30 of 97 +yx:=solve(ode361,y,x) +--R +--R +--R (30) +--R y(x) 2 y(x) y(x) +--R 2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----) - cos(x y(x)) +--R 2 2 2 +--R + +--R cos(y(x)) +--R Type: Union(Expression Integer,...) +--E 30 + +--S 31 of 97 +ode361expr:=(x*sin(x*yx)+cos(x+yx)-sin(yx))*D(yx,x)+_ + yx*sin(x*yx)+cos(x+yx)+cos(x) +--R +--R +--R (31) +--R 2 y(x) 2 +--R x sin(x y(x)) - x sin(y(x)) + x cos(y(x) + x)sin(----) +--R 2 +--R + +--R y(x) 2 +--R x cos(----) cos(y(x) + x) +--R 2 +--R * +--R , +--R y (x) +--R +--R + +--R y(x) y(x) y(x) 2 +--R x y(x)sin(x y(x)) + (2x cos(----)sin(----) + 2cos(----) )sin(y(x) + x) +--R 2 2 2 +--R + +--R y(x) y(x) +--R - 2cos(----)cos(y(x) + x)sin(----) - cos(x y(x)) +--R 2 2 +--R + +--R y(x) 2 +--R 2x cos(----) cos(y(x) + x) + cos(y(x)) +--R 2 +--R * +--R sin +--R y(x) 2 y(x) y(x) +--R 2x cos(----) sin(y(x) + x) - 2x cos(----)cos(y(x) + x)sin(----) +--R 2 2 2 +--R + +--R - x cos(x y(x)) + x cos(y(x)) +--R + +--R y(x) 2 +--R - x sin(x y(x)) + sin(y(x)) - cos(y(x) + x)sin(----) +--R 2 +--R + +--R y(x) 2 +--R - cos(----) cos(y(x) + x) +--R 2 +--R * +--R , +--R y (x) +--R +--R + +--R y(x) y(x) +--R - y(x)sin(x y(x)) - 2cos(----)sin(----)sin(y(x) + x) +--R 2 2 +--R + +--R y(x) 2 +--R - 2cos(----) cos(y(x) + x) +--R 2 +--R * +--R sin +--R y(x) 2 y(x) y(x) +--R 2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----) +--R 2 2 2 +--R + +--R - cos(x y(x)) + cos(y(x)) +--R + +--R y(x) 2 +--R x sin(x y(x)) - sin(y(x)) + cos(y(x) + x)sin(----) +--R 2 +--R + +--R y(x) 2 +--R cos(----) cos(y(x) + x) +--R 2 +--R * +--R , +--R y (x) +--R +--R + +--R y(x) y(x) +--R y(x)sin(x y(x)) + 2cos(----)sin(----)sin(y(x) + x) +--R 2 2 +--R + +--R y(x) 2 +--R 2cos(----) cos(y(x) + x) + 1 +--R 2 +--R * +--R cos +--R y(x) 2 y(x) y(x) +--R 2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----) +--R 2 2 2 +--R + +--R - cos(x y(x)) + cos(y(x)) + x +--R + +--R cos(x) +--R Type: Expression Integer +--E 31 + +--S 32 of 97 +ode363 := (x*D(y(x),x)-y(x))*cos(y(x)/x)**2+x +--R +--R +--R y(x) 2 , y(x) 2 +--R (32) x cos(----) y (x) - y(x)cos(----) + x +--R x x +--R Type: Expression Integer +--E 32 + +--S 33 of 97 +yx:=solve(ode363,y,x) +--R +--R +--R y(x) y(x) +--R x cos(----)sin(----) + 2x log(x) + y(x) +--R x x +--R (33) --------------------------------------- +--R 2x +--R Type: Union(Expression Integer,...) +--E 33 + +--S 34 of 97 +ode363expr := (x*D(yx,x)-yx)*cos(yx/x)**2+x +--R +--R +--R (34) +--R y(x) 2 y(x) 2 , y(x) 2 +--R (- x sin(----) + x cos(----) + x)y (x) + y(x)sin(----) +--R x x x +--R + +--R y(x) y(x) y(x) 2 +--R - x cos(----)sin(----) - y(x)cos(----) - 2x log(x) - 2y(x) + 2x +--R x x x +--R * +--R y(x) y(x) 2 +--R x cos(----)sin(----) + 2x log(x) + y(x) +--R x x +--R cos(---------------------------------------) +--R 2 +--R 2x +--R + +--R 2 +--R 2x +--R / +--R 2x +--R Type: Expression Integer +--E 34 + +--S 35 of 97 +ode364 := (y(x)*sin(y(x)/x)-x*cos(y(x)/x))*x*D(y(x),x)-_ + (x*cos(y(x)/x)+y(x)*sin(y(x)/x))*y(x) +--R +--R +--R (35) +--R y(x) 2 y(x) , 2 y(x) y(x) +--R (x y(x)sin(----) - x cos(----))y (x) - y(x) sin(----) - x y(x)cos(----) +--R x x x x +--R Type: Expression Integer +--E 35 + +--S 36 of 97 +yx:=solve(ode364,y,x) +--R +--R +--R y(x) +--R (36) - x y(x)cos(----) +--R x +--R Type: Union(Expression Integer,...) +--E 36 + +--S 37 of 97 +ode364expr := (yx*sin(yx/x)-x*cos(yx/x))*x*D(yx,x)-_ + (x*cos(yx/x)+yx*sin(yx/x))*yx +--R +--R +--R (37) +--R 2 2 y(x) y(x) 3 y(x) 2 , +--R (x y(x) cos(----)sin(----) - x y(x)cos(----) )y (x) +--R x x x +--R + +--R 3 y(x) y(x) +--R - x y(x) cos(----)sin(----) +--R x x +--R * +--R y(x) +--R sin(y(x)cos(----)) +--R x +--R + +--R 2 y(x) 3 y(x) , 2 y(x) +--R (- x y(x)sin(----) + x cos(----))y (x) + x y(x) sin(----) +--R x x x +--R + +--R 2 y(x) +--R 2x y(x)cos(----) +--R x +--R * +--R y(x) +--R cos(y(x)cos(----)) +--R x +--R Type: Expression Integer +--E 37 + +--S 38 of 97 +ode434 := D(y(x),x)-1 +--R +--R +--R , +--R (38) y (x) - 1 +--R +--R Type: Expression Integer +--E 38 + +--S 39 of 97 +ode434a:=solve(ode434,y,x) +--R +--R +--R (39) [particular= x,basis= ] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 39 + +--S 40 of 97 +yx:=ode434a.particular +--R +--R +--R (40) x +--R Type: Expression Integer +--E 40 + +--S 41 of 97 +ode434expr := D(yx,x)-1 +--R +--R +--R (41) 0 +--R Type: Expression Integer +--E 41 + +--S 42 of 97 +ode683 := (D(y(x),x) = y(x)*(-1+log(x*(x+1))*y(x)*x**4-log(x*(x+1))*x**3)/x) +--R +--R +--R 4 2 3 2 +--R , (x y(x) - x y(x))log(x + x) - y(x) +--R (42) y (x)= ------------------------------------ +--R x +--R Type: Equation Expression Integer +--E 42 + +--S 43 of 97 +solve(ode683,y,x) +--R +--R +--R - x y(x) + 1 +--R (43) ----------------------------------------------- +--R 3 2 3 2 +--R 6x log(x + x) - 4x + 3x - 6x +--R ------------------------------- +--R 3+-----+ 18 +--R x y(x)\|x + 1 %e +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 97 +ode703 := (D(y(x),x) = y(x)*(1-x+y(x)*x**2*log(x)+y(x)*x**3-x*log(x)-x**2)/_ + (x-1)/x) +--R +--R +--R 2 2 3 2 2 +--R , (x y(x) - x y(x))log(x) + x y(x) + (- x - x + 1)y(x) +--R (44) y (x)= ------------------------------------------------------- +--R 2 +--R x - x +--R Type: Equation Expression Integer +--E 44 + +--S 45 of 97 +solve(ode703,y,x) +--R +--R +--R - x y(x) + 1 +--R (45) ---------------------------- +--R 2 - dilog(x) + x +--R (x - x)y(x)%e +--R Type: Union(Expression Integer,...) +--E 45 + +--S 46 of 97 +ode714 := (D(y(x),x) = -y(x)*(-log(1/x)+exp(x)+y(x)*x**2*log(x)+_ + y(x)*x**3-x*log(x)-x**2)/(-log(1/x)+exp(x))/x) +--R +--R +--R (46) +--R 2 2 1 x 3 2 2 +--R (x y(x) - x y(x))log(x) - y(x)log(-) + y(x)%e + x y(x) - x y(x) +--R , x +--R y (x)= ------------------------------------------------------------------ +--R 1 x +--R x log(-) - x %e +--R x +--R Type: Equation Expression Integer +--E 46 + +--S 47 of 97 +solve(ode714,y,x) +--R +--R +--R (47) +--R - +--I 1 %I 2 +--I x %I log(%I) + log(--) - %e + %I +--I ++ %I +--I | --------------------------------- d%I +--I ++ 1 %I +--I %I log(--) - %I %e +--I %I +--R y(x)%e +--R * +--R INTSIGN +--R , +--R x +--R , +--R 2 +--I - %I log(%I) - %I +--R -------------------------------------------------------------- +--I 1 %I 2 +--I %I %I log(%I) + log(--) - %e + %I +--I ++ %I +--I | --------------------------------- d%I +--I ++ 1 %I +--I %I log(--) - %I %e +--I 1 %I %I +--R (log(--) - %e )%e +--I %I +--R * +--I d%I +--R + +--R 1 +--R / +--I 1 %I 2 +--I x %I log(%I) + log(--) - %e + %I +--I ++ %I +--I | --------------------------------- d%I +--I ++ 1 %I +--I %I log(--) - %I %e +--I %I +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 47 + +--S 48 of 97 +ode719 := (D(y(x),x) = y(x)*(-exp(x)+log(2*x)*x**2*y(x)-log(2*x)*x)/x/exp(x)) +--R +--R +--R 2 2 x +--R , (x y(x) - x y(x))log(2x) - y(x)%e +--R (48) y (x)= ----------------------------------- +--R x +--R x %e +--R Type: Equation Expression Integer +--E 48 + +--S 49 of 97 +solve(ode719,y,x) +--R +--R +--R - x y(x) + 1 +--R (49) ---------------------------------- +--I x %I +--I ++ %I log(2%I) + %e +--I | ------------------ d%I +--I ++ %I +--I %I %e +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 49 + +--S 50 of 97 +ode736 := (D(y(x),x) = (2*x**2+2*x+x**4-2*y(x)*x**2-1+y(x)**2)/(x+1)) +--R +--R +--R 2 2 4 2 +--R , y(x) - 2x y(x) + x + 2x + 2x - 1 +--R (50) y (x)= ----------------------------------- +--R x + 1 +--R Type: Equation Expression Integer +--E 50 + +--S 51 of 97 +solve(ode736,y,x) +--R +--R +--R 2 4 3 2 +--R (x + 2x - 2)y(x) - x - 2x + 3x + 2x + 4 +--R (51) ------------------------------------------- +--R 2 +--R 2y(x) - 2x - 2 +--R Type: Union(Expression Integer,...) +--E 51 + +--S 52 of 97 +ode765 := (D(y(x),x) = y(x)*(-1-log((x-1)*(1+x)/x)+_ + log((x-1)*(1+x)/x)*x*y(x))/x) +--R +--R +--R 2 +--R 2 x - 1 +--R (x y(x) - y(x))log(------) - y(x) +--R , x +--R (52) y (x)= ---------------------------------- +--R x +--R Type: Equation Expression Integer +--E 52 + +--S 53 of 97 +solve(ode765,y,x) +--R +--R +--R - x y(x) + 1 +--R (53) -------------------------------- +--R 2 +--I %I - 1 +--R x log(-------) + 1 +--I ++ %I +--I | ---------------- d%I +--I ++ %I +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 53 + +--S 54 of 97 +ode766 := (D(y(x),x) = y(x)*(-log(x)-x*log((x-1)*(1+x)/x)+_ + log((x-1)*(1+x)/x)*x**2*y(x))/x/log(x)) +--R +--R +--R 2 +--R 2 2 x - 1 +--R - y(x)log(x) + (x y(x) - x y(x))log(------) +--R , x +--R (54) y (x)= -------------------------------------------- +--R x log(x) +--R Type: Equation Expression Integer +--E 54 + +--S 55 of 97 +solve(ode766,y,x) +--R +--R +--R (55) +--R - +--R 2 +--I %I - 1 +--I x log(%I) + %I log(-------) +--I ++ %I +--I | ------------------------- d%I +--I ++ %I log(%I) +--R y(x)%e +--R * +--R 2 +--I %I - 1 +--I x %I log(-------) +--I ++ %I +--I | - --------------------------------------------- d%I +--R ++ 2 +--I %I - 1 +--I %I log(%I) + %I log(-------) +--I ++ %I +--I | ------------------------- d%I +--I ++ %I log(%I) +--I log(%I)%e +--R + +--R 1 +--R / +--R 2 +--I %I - 1 +--I x log(%I) + %I log(-------) +--I ++ %I +--I | ------------------------- d%I +--I ++ %I log(%I) +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 55 + +--S 56 of 97 +ode776 := (D(y(x),x) = y(x)*(-log(1/x)-log((x**2+1)/x)*x+_ + log((x**2+1)/x)*x**2*y(x))/x/log(1/x)) +--R +--R +--R 2 +--R 2 2 x + 1 1 +--R (x y(x) - x y(x))log(------) - y(x)log(-) +--R , x x +--R (56) y (x)= ------------------------------------------ +--R 1 +--R x log(-) +--R x +--R Type: Equation Expression Integer +--E 56 + +--S 57 of 97 +solve(ode776,y,x) +--R +--R +--R - x y(x) + 1 +--R (57) ----------------------------------------- +--R 2 +--I %I + 1 1 +--I x %I log(-------) + log(--) +--I ++ %I %I +--I | ------------------------- d%I +--R ++ 1 +--I %I log(--) +--I %I +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 57 + +--S 58 of 97 +ode872 := (D(y(x),x) = 1/5*(-30*y(x)*x**3+12*x**6+70*x**(7/2)-30*x**3-_ + 25*y(x)*x**(1/2)+50*x-25*x**(1/2)-25)/_ + (-5*y(x)+2*x**3+10*x**(1/2)-5)/x) +--R +--R +--R 3 +-+ 3 6 3 +--R , (- 25y(x) + 70x - 25)\|x - 30x y(x) + 12x - 30x + 50x - 25 +--R (58) y (x)= -------------------------------------------------------------- +--R +-+ 4 +--R 50x\|x - 25x y(x) + 10x - 25x +--R Type: Equation Expression Integer +--E 58 + +--S 59 of 97 +solve(ode872,y,x) +--R +--R +--R (59) +--R +-+ 3 +-+ 2 3 +--R 100log(\|x ) + (100y(x) - 40x + 100)\|x - 25y(x) + (20x - 50)y(x) +--R + +--R 6 3 +--R - 4x + 20x - 100x +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 59 + +--S 60 of 97 +ode555 := sqrt(D(y(x),x)**2+1)+x*D(y(x),x)-y(x) +--R +--R +--R +----------+ +--R | , 2 , +--R (60) |y (x) + 1 + xy (x) - y(x) +--R \| +--R Type: Expression Integer +--E 60 + +--S 61 of 97 +solve(ode555,y,x) +--R +--R +--R +-----------+ +--R | , 2 +--I x |y (%I) + 1 - y(x) +--R ++ \| +--I (61) | --------------------- d%I +--R ++ 2 +--I %I +--R Type: Union(Expression Integer,...) +--E 61 + +--S 62 of 97 +ode557 := x*(sqrt(D(y(x),x)**2+1)+D(y(x),x))-y(x) +--R +--R +--R +----------+ +--R | , 2 , +--R (62) x |y (x) + 1 + xy (x) - y(x) +--R \| +--R Type: Expression Integer +--E 62 + +--S 63 of 97 +solve(ode557,y,x) +--R +--R +--R +-----------+ +--R | , 2 +--I x %I |y (%I) + 1 - y(x) +--R ++ \| +--I (63) | ----------------------- d%I +--R ++ 2 +--I %I +--R Type: Union(Expression Integer,...) +--E 63 + +--S 64 of 97 +ode558 := a*x*sqrt(D(y(x),x)**2+1)+x*D(y(x),x)-y(x) +--R +--R +--R +----------+ +--R | , 2 , +--R (64) a x |y (x) + 1 + xy (x) - y(x) +--R \| +--R Type: Expression Integer +--E 64 + +--S 65 of 97 +solve(ode558,y,x) +--R +--R +--R +-----------+ +--R | , 2 +--I x %I a |y (%I) + 1 - y(x) +--R ++ \| +--I (65) | ------------------------- d%I +--R ++ 2 +--I %I +--R Type: Union(Expression Integer,...) +--E 65 + +--S 66 of 97 +ode562 := a*(D(y(x),x)**3+1)**(1/3)+b*x*D(y(x),x)-y(x) +--R +--R +--R +----------+ +--R | , 3 , +--R (66) a 3|y (x) + 1 + b xy (x) - y(x) +--R \| +--R Type: Expression Integer +--E 66 + +--S 67 of 97 +solve(ode562,y,x) +--R +--R +--I log(%I) log(%I) +--R - ------- +-----------+ - ------- +--R b | , 3 b +--I x a %e 3|y (%I) + 1 - y(x)%e +--R ++ \| +--I (67) | --------------------------------------------- d%I +--I ++ %I +--R Type: Union(Expression Integer,...) +--E 67 + +--S 68 of 97 +ode563 := log(D(y(x),x))+x*D(y(x),x)+a*y(x)+b +--R +--R +--R , , +--R (68) log(y (x)) + xy (x) + a y(x) + b +--R +--R Type: Expression Integer +--E 68 + +--S 69 of 97 +solve(ode563,y,x) +--R +--R +--I a log(%I) , a log(%I) +--I x %e log(y (%I)) + (a y(x) + b)%e +--R ++ +--I (69) | ------------------------------------------------ d%I +--I ++ %I +--R Type: Union(Expression Integer,...) +--E 69 + +--S 70 of 97 +ode564 := log(D(y(x),x))+a*(x*D(y(x),x)-y(x)) +--R +--R +--R , , +--R (70) log(y (x)) + a xy (x) - a y(x) +--R +--R Type: Expression Integer +--E 70 + +--S 71 of 97 +solve(ode564,y,x) +--R +--R +--R , +--I x log(y (%I)) - a y(x) +--R ++ +--I (71) | -------------------- d%I +--R ++ 2 +--I %I +--R Type: Union(Expression Integer,...) +--E 71 + +--S 72 of 97 +ode571 := a*x**n*f(D(y(x),x))+x*D(y(x),x)-y(x) +--R +--R +--R n , , +--R (72) a x f(y (x)) + xy (x) - y(x) +--R +--R Type: Expression Integer +--E 72 + +--S 73 of 97 +solve(ode571,y,x) +--R +--R +--R n , +--I x a %I f(y (%I)) - y(x) +--R ++ +--I (73) | --------------------- d%I +--R ++ 2 +--I %I +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 97 +ode573 := f(x*D(y(x),x)**2)+2*x*D(y(x),x)-y(x) +--R +--R +--R , 2 , +--R (74) f(x y (x) ) + 2xy (x) - y(x) +--R +--R Type: Expression Integer +--E 74 + +--S 75 of 97 +solve(ode573,y,x) +--R +--R +--R , 2 +--I x f(%I y (%I) ) - y(x) +--R ++ +--I (75) | -------------------- d%I +--R ++ +--+ +--I %I\|%I +--R Type: Union(Expression Integer,...) +--E 75 + +--S 76 of 97 +ode683 := (D(y(x),x) = y(x)*(-1+log(x*(x+1))*y(x)*x**4-log(x*(x+1))*x**3)/x) +--R +--R +--R 4 2 3 2 +--R , (x y(x) - x y(x))log(x + x) - y(x) +--R (76) y (x)= ------------------------------------ +--R x +--R Type: Equation Expression Integer +--E 76 + +--S 77 of 97 +solve(ode683,y,x) +--R +--R +--R - x y(x) + 1 +--R (77) ----------------------------------------------- +--R 3 2 3 2 +--R 6x log(x + x) - 4x + 3x - 6x +--R ------------------------------- +--R 3+-----+ 18 +--R x y(x)\|x + 1 %e +--R Type: Union(Expression Integer,...) +--E 77 + +--S 78 of 97 +ode703 := (D(y(x),x) = y(x)*(1-x+y(x)*x**2*log(x)+y(x)*x**3-x*log(x)-x**2)/_ + (x-1)/x) +--R +--R +--R 2 2 3 2 2 +--R , (x y(x) - x y(x))log(x) + x y(x) + (- x - x + 1)y(x) +--R (78) y (x)= ------------------------------------------------------- +--R 2 +--R x - x +--R Type: Equation Expression Integer +--E 78 + +--S 79 of 97 +solve(ode703,y,x) +--R +--R +--R - x y(x) + 1 +--R (79) ---------------------------- +--R 2 - dilog(x) + x +--R (x - x)y(x)%e +--R Type: Union(Expression Integer,...) +--E 79 + +--S 80 of 97 +ode714 := (D(y(x),x) = -y(x)*(-log(1/x)+exp(x)+y(x)*x**2*log(x)+_ + y(x)*x**3-x*log(x)-x**2)/(-log(1/x)+exp(x))/x) +--R +--R +--R (80) +--R 2 2 1 x 3 2 2 +--R (x y(x) - x y(x))log(x) - y(x)log(-) + y(x)%e + x y(x) - x y(x) +--R , x +--R y (x)= ------------------------------------------------------------------ +--R 1 x +--R x log(-) - x %e +--R x +--R Type: Equation Expression Integer +--E 80 + +--S 81 of 97 +solve(ode714,y,x) +--R +--R +--R (81) +--R - +--I 1 %I 2 +--I x %I log(%I) + log(--) - %e + %I +--I ++ %I +--I | --------------------------------- d%I +--I ++ 1 %I +--I %I log(--) - %I %e +--I %I +--R y(x)%e +--R * +--R INTSIGN +--R , +--R x +--R , +--R 2 +--I - %I log(%I) - %I +--R -------------------------------------------------------------- +--I 1 %I 2 +--I %I %I log(%I) + log(--) - %e + %I +--I ++ %I +--I | --------------------------------- d%I +--I ++ 1 %I +--I %I log(--) - %I %e +--I 1 %I %I +--R (log(--) - %e )%e +--I %I +--R * +--I d%I +--R + +--R 1 +--R / +--I 1 %I 2 +--I x %I log(%I) + log(--) - %e + %I +--I ++ %I +--I | --------------------------------- d%I +--I ++ 1 %I +--I %I log(--) - %I %e +--I %I +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 81 + +--S 82 of 97 +ode719 := (D(y(x),x) = y(x)*(-exp(x)+log(2*x)*x**2*y(x)-log(2*x)*x)/x/exp(x)) +--R +--R +--R 2 2 x +--R , (x y(x) - x y(x))log(2x) - y(x)%e +--R (82) y (x)= ----------------------------------- +--R x +--R x %e +--R Type: Equation Expression Integer +--E 82 + +--S 83 of 97 +solve(ode719,y,x) +--R +--R +--R - x y(x) + 1 +--R (83) ---------------------------------- +--I x %I +--I ++ %I log(2%I) + %e +--I | ------------------ d%I +--I ++ %I +--I %I %e +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 of 97 +ode736 := (D(y(x),x) = (2*x**2+2*x+x**4-2*y(x)*x**2-1+y(x)**2)/(x+1)) +--R +--R +--R 2 2 4 2 +--R , y(x) - 2x y(x) + x + 2x + 2x - 1 +--R (84) y (x)= ----------------------------------- +--R x + 1 +--R Type: Equation Expression Integer +--E 84 + +--S 85 of 97 +solve(ode736,y,x) +--R +--R +--R 2 4 3 2 +--R (x + 2x - 2)y(x) - x - 2x + 3x + 2x + 4 +--R (85) ------------------------------------------- +--R 2 +--R 2y(x) - 2x - 2 +--R Type: Union(Expression Integer,...) +--E 85 + +--S 86 of 97 +ode765 := (D(y(x),x) = y(x)*(-1-log((x-1)*(1+x)/x)+_ + log((x-1)*(1+x)/x)*x*y(x))/x) +--R +--R +--R 2 +--R 2 x - 1 +--R (x y(x) - y(x))log(------) - y(x) +--R , x +--R (86) y (x)= ---------------------------------- +--R x +--R Type: Equation Expression Integer +--E 86 + +--S 87 of 97 +solve(ode765,y,x) +--R +--R +--R - x y(x) + 1 +--R (87) -------------------------------- +--R 2 +--I %I - 1 +--R x log(-------) + 1 +--I ++ %I +--I | ---------------- d%I +--I ++ %I +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 87 + +--S 88 of 97 +ode766 := (D(y(x),x) = y(x)*(-log(x)-x*log((x-1)*(1+x)/x)+_ + log((x-1)*(1+x)/x)*x**2*y(x))/x/log(x)) +--R +--R +--R 2 +--R 2 2 x - 1 +--R - y(x)log(x) + (x y(x) - x y(x))log(------) +--R , x +--R (88) y (x)= -------------------------------------------- +--R x log(x) +--R Type: Equation Expression Integer +--E 88 + +--S 89 of 97 +solve(ode766,y,x) +--R +--R +--R (89) +--R - +--R 2 +--I %I - 1 +--I x log(%I) + %I log(-------) +--I ++ %I +--I | ------------------------- d%I +--I ++ %I log(%I) +--R y(x)%e +--R * +--R 2 +--I %I - 1 +--I x %I log(-------) +--I ++ %I +--I | - --------------------------------------------- d%I +--R ++ 2 +--I %I - 1 +--I %I log(%I) + %I log(-------) +--I ++ %I +--I | ------------------------- d%I +--I ++ %I log(%I) +--I log(%I)%e +--R + +--R 1 +--R / +--R 2 +--I %I - 1 +--I x log(%I) + %I log(-------) +--I ++ %I +--I | ------------------------- d%I +--I ++ %I log(%I) +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 89 + +--S 90 of 97 +ode776 := (D(y(x),x) = y(x)*(-log(1/x)-log((x**2+1)/x)*x+_ + log((x**2+1)/x)*x**2*y(x))/x/log(1/x)) +--R +--R +--R 2 +--R 2 2 x + 1 1 +--R (x y(x) - x y(x))log(------) - y(x)log(-) +--R , x x +--R (90) y (x)= ------------------------------------------ +--R 1 +--R x log(-) +--R x +--R Type: Equation Expression Integer +--E 90 + +--S 91 of 97 +solve(ode776,y,x) +--R +--R +--R - x y(x) + 1 +--R (91) ----------------------------------------- +--R 2 +--I %I + 1 1 +--I x %I log(-------) + log(--) +--I ++ %I %I +--I | ------------------------- d%I +--R ++ 1 +--I %I log(--) +--I %I +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 91 + +--S 92 of 97 +ode872 := (D(y(x),x) = 1/5*(-30*y(x)*x**3+12*x**6+70*x**(7/2)-30*x**3-_ + 25*y(x)*x**(1/2)+50*x-25*x**(1/2)-25)/(-5*y(x)+2*x**3+_ + 10*x**(1/2)-5)/x) +--R +--R +--R 3 +-+ 3 6 3 +--R , (- 25y(x) + 70x - 25)\|x - 30x y(x) + 12x - 30x + 50x - 25 +--R (92) y (x)= -------------------------------------------------------------- +--R +-+ 4 +--R 50x\|x - 25x y(x) + 10x - 25x +--R Type: Equation Expression Integer +--E 92 + +--S 93 of 97 +solve(ode872,y,x) +--R +--R +--R (93) +--R +-+ 3 +-+ 2 3 +--R 100log(\|x ) + (100y(x) - 40x + 100)\|x - 25y(x) + (20x - 50)y(x) +--R + +--R 6 3 +--R - 4x + 20x - 100x +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 93 + +--S 94 of 97 +ode956 := (D(y(x),x) = 1/(1+log(x))*y(x)*(-1-x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*x**2-x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*x**2*log(x)+x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*x**2*y(x)+2*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*x**2*y(x)*log(x)+x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*x**2*y(x)*log(x)**2)/x) +--R +--R +--R (94) +--R , +--R y (x) = +--R +--R 2 2 2 2 2 2 2 2 2 +--R (x y(x) log(x) + (2x y(x) - x y(x))log(x) + x y(x) - x y(x)) +--R * +--R 2 +--R 2log(x) 2 +--R ---------- ---------- +--R log(x) + 1 log(x) + 1 +--R %e x +--R + +--R - y(x) +--R / +--R x log(x) + x +--R Type: Equation Expression Integer +--E 94 + +--S 95 of 97 +solve(ode956,y,x) +--R +--R +--R - y(x)log(x) - y(x) + 1 +--R (95) ------------------------- +--R 4 4 +--R x x +--R -- -- +--R 4 4 +--R y(x)%e log(x) + y(x)%e +--R Type: Union(Expression Integer,...) +--E 95 + +--S 96 of 97 +ode957 := (D(y(x),x) = 1/(1+log(x))*y(x)*(-1-x**3*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)-x**3*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*log(x)+x**3*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*y(x)+2*x**3*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*y(x)*log(x)+x**3*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*y(x)*log(x)**2)/x) +--R +--R +--R (96) +--R , +--R y (x) = +--R +--R 3 2 2 3 2 3 3 2 3 +--R (x y(x) log(x) + (2x y(x) - x y(x))log(x) + x y(x) - x y(x)) +--R * +--R 2 +--R 2log(x) 2 +--R ---------- ---------- +--R log(x) + 1 log(x) + 1 +--R %e x +--R + +--R - y(x) +--R / +--R x log(x) + x +--R Type: Equation Expression Integer +--E 96 + +--S 97 of 97 +solve(ode957,y,x) +--R +--R +--R - y(x)log(x) - y(x) + 1 +--R (97) ------------------------- +--R 5 5 +--R x x +--R -- -- +--R 5 5 +--R y(x)%e log(x) + y(x)%e +--R Type: Union(Expression Integer,...) +--E 97 +)spool +)lisp (bye) +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} {\bf http://www.cs.uwaterloo.ca/$\tilde{}$ecterrab/odetools.html} +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/kamke7.input.pdf b/src/axiom-website/CATS/kamke7.input.pdf new file mode 100644 index 0000000..c3054c2 Binary files /dev/null and b/src/axiom-website/CATS/kamke7.input.pdf differ