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[Axiom-developer] 20071005.02.tpd.patch
|
From: |
daly |
|
Subject: |
[Axiom-developer] 20071005.02.tpd.patch |
|
Date: |
Fri, 5 Oct 2007 02:23:32 -0500 |
This patch adds Axiom regression tests of Kamke ODEs 151-200
======================================================================
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}
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