diff --git a/changelog b/changelog index c71345c..2e818cc 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,5 @@ +20071005 tpd src/input/Makefile kamke3.input regression test added +20071005 tpd src/input/kamke3.input ODE regression test added 20071004 tpd src/input/Makefile kamke2.input regression test added 20071004 tpd src/input/kamke2.input ODE regression test added 20071004 tpd src/input/Makefile kamke1.input regression test added diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 1bfbcc1..1bda3be 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -322,7 +322,7 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress alist.regress \ intmix2.regress intmix.regress int.regress intrf.regress \ iprntpk.regress \ ipftest.regress is.regress isprime.regress kafile.regress \ - kamke0.regress kamke1.regress kamke2.regress \ + kamke0.regress kamke1.regress kamke2.regress kamke3.regress \ kernel.regress knot2.regress kovacic.regress kuipers.regress \ laplace.regress leg.regress limit.regress lindep.regress \ list.regress lode.regress lodesys.regress lodo1.regress \ @@ -562,7 +562,7 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input ${OUT}/algfacob.input \ ${OUT}/intlf.input ${OUT}/intmix.input ${OUT}/intrf.input \ ${OUT}/ipftest.input ${OUT}/is.input ${OUT}/isprime.input \ ${OUT}/kafile.input ${OUT}/kamke0.input ${OUT}/kamke1.input \ - ${OUT}/kamke2.input \ + ${OUT}/kamke2.input ${OUT}/kamke3.input \ ${OUT}/kernel.input ${OUT}/knot.input \ ${OUT}/kovacic.input ${OUT}/kuipers.input \ ${OUT}/laplace.input ${OUT}/leg.input ${OUT}/lexp.input \ @@ -829,7 +829,7 @@ DOCFILES= \ ${DOC}/ipftest.input.dvi ${DOC}/is.input.dvi \ ${DOC}/isprime.input.dvi ${DOC}/kafile.input.dvi \ ${DOC}/kamke0.input.dvi ${DOC}/kamke1.input.dvi \ - ${DOC}/kamke2.input.dvi \ + ${DOC}/kamke2.input.dvi ${DOC}/kamke3.input.dvi \ ${DOC}/kernel.input.dvi ${DOC}/knot2.input.dvi \ ${DOC}/knot.input.dvi ${DOC}/knownbugs.input.dvi \ ${DOC}/kovacic.input.dvi ${DOC}/kuipers.input.dvi \ diff --git a/src/input/kamke3.input.pamphlet b/src/input/kamke3.input.pamphlet new file mode 100644 index 0000000..2d9ac94 --- /dev/null +++ b/src/input/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 +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}