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[Axiom-developer] 20071005.01.tpd.patch
|
From: |
daly |
|
Subject: |
[Axiom-developer] 20071005.01.tpd.patch |
|
Date: |
Thu, 4 Oct 2007 23:21:37 -0500 |
This patch adds Axiom regression tests of Kamke ODEs 101-150
====================================================================
diff --git a/changelog b/changelog
index 44f04bc..c71345c 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+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
20071004 tpd src/input/kamke1.input ODE regression test added
20071004 tpd src/input/Makefile kamke0.input regression test added
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index 159377a..1bfbcc1 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 \
+ kamke0.regress kamke1.regress kamke2.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 \
@@ -562,6 +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}/kernel.input ${OUT}/knot.input \
${OUT}/kovacic.input ${OUT}/kuipers.input \
${OUT}/laplace.input ${OUT}/leg.input ${OUT}/lexp.input \
@@ -828,6 +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}/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/kamke2.input.pamphlet b/src/input/kamke2.input.pamphlet
new file mode 100644
index 0000000..2c8be63
--- /dev/null
+++ b/src/input/kamke2.input.pamphlet
@@ -0,0 +1,1731 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input kamke2.input}
+\author{Timothy Daly}
+\maketitle
+\begin{abstract}
+This is the 50 ODEs of the Kamke test suite as published by
+E. S. Cheb-Terrab\cite{1}. They have been rewritten using Axiom
+syntax. Where possible we show that the particular solution actually
+satisfies the original ordinary differential equation.
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+<<*>>=
+)spool kamke2.output
+)set break resume
+)set mes auto off
+)clear all
+
+--S 1 of 131
+y:=operator 'y
+--R
+--R (1) y
+--R Type:
BasicOperator
+--E 1
+
+--S 2 of 131
+f:=operator 'f
+--R
+--R (2) f
+--R Type:
BasicOperator
+--E 2
+
+--S 3 of 131
+g:=operator 'g
+--R
+--R (3) g
+--R Type:
BasicOperator
+--E 3
+
+--S 4 of 131
+ode101 := x*D(y(x),x) + x*y(x)**2 - y(x)
+--R
+--R , 2
+--R (4) xy (x) + x y(x) - y(x)
+--R
+--R Type: Expression
Integer
+--E 4
+
+--S 5 of 131
+yx:=solve(ode101,y,x)
+--R
+--R 2
+--R x y(x) - 2x
+--R (5) -----------
+--R 2y(x)
+--R Type: Union(Expression
Integer,...)
+--E 5
+
+--S 6 of 131
+ode101expr := x*D(yx,x) + x*yx**2 - yx
+--R
+--R 2 , 5 2 2 4 3
+--R 4x y (x) + (x + 2x )y(x) - 4x y(x) + 4x
+--R
+--R (6) ------------------------------------------
+--R 2
+--R 4y(x)
+--R Type: Expression
Integer
+--E 6
+
+--S 7 of 131
+ode102 := x*D(y(x),x) + x*y(x)**2 - y(x) - a*x**3
+--R
+--R , 2 3
+--R (7) xy (x) + x y(x) - y(x) - a x
+--R
+--R Type: Expression
Integer
+--E 7
+
+--S 8 of 131
+yx:=solve(ode102,y,x)
+--R
+--R +-+
+--R (2y(x) + 3x)\|a + 3y(x) + 2a x
+--R (8) ---------------------------------------------
+--R 2 +-+
+--R +-+ x \|a
+--R ((6y(x) - 4a x)\|a + 4a y(x) - 6a x)%e
+--R Type: Union(Expression
Integer,...)
+--E 8
+
+--S 9 of 131
+ode102expr := x*D(yx,x) + x*yx**2 - yx - a*x**3
+--R
+--R (9)
+--R 2 2 3 2 3 +-+
+--R ((- 144a - 108a)x y(x) + (32a + 216a )x )\|a
+--R +
+--R 3 2 2 3 2 3
+--R (- 32a - 216a )x y(x) + (144a + 108a )x
+--R *
+--R 2 +-+
+--R x \|a ,
+--R %e y (x)
+--R
+--R +
+--R 3 2 3 3 4 3 4 2
+--R (- 144a - 108a )x y(x) + (96a + 648a )x y(x)
+--R +
+--R 4 3 5 5 4 6
+--R (- 432a - 324a )x y(x) + (32a + 216a )x
+--R *
+--R +-+
+--R \|a
+--R +
+--R 4 3 3 3 4 3 4 2
+--R (- 32a - 216a )x y(x) + (432a + 324a )x y(x)
+--R +
+--R 5 4 5 5 4 6
+--R (- 96a - 648a )x y(x) + (144a + 108a )x
+--R *
+--R 2 +-+ 2
+--R x \|a
+--R (%e )
+--R +
+--R 2 2 2 3
+--R ((- 144a - 108a)x - 16a - 108a)y(x)
+--R +
+--R 3 2 3 2 2
+--R ((32a + 216a )x + (216a + 162a)x)y(x)
+--R +
+--R 3 2 4 3 2 2 4
3 5
+--R ((144a + 108a )x + (- 16a - 108a )x )y(x) + (- 32a -
216a )x
+--R +
+--R 3 2 3
+--R (- 72a - 54a )x
+--R *
+--R +-+
+--R \|a
+--R +
+--R 3 2 2 2 3
+--R ((- 32a - 216a )x - 72a - 54a)y(x)
+--R +
+--R 3 2 3 3 2 2
+--R ((144a + 108a )x + (48a + 324a )x)y(x)
+--R +
+--R 4 3 4 3 2 2 4 3 5
+--R ((32a + 216a )x + (- 72a - 54a )x )y(x) + (- 144a - 108a )x
+--R +
+--R 4 3 3
+--R (- 16a - 108a )x
+--R *
+--R 2 +-+
+--R x \|a
+--R %e
+--R +
+--R 3 2 2 2 2 3
+--R (36a + 27)x y(x) + (8a + 54a)x y(x) + (- 36a - 27a)x y(x)
+--R +
+--R 3 2 4
+--R (- 8a - 54a )x
+--R *
+--R +-+
+--R \|a
+--R +
+--R 2 3 2 2 2 3 2 3
+--R (8a + 54a)x y(x) + (36a + 27a)x y(x) + (- 8a - 54a )x y(x)
+--R +
+--R 3 2 4
+--R (- 36a - 27a )x
+--R /
+--R 2 3 3 2 2
+--R (144a + 108a)y(x) + (- 96a - 648a )x y(x)
+--R +
+--R 3 2 2 4 3 3
+--R (432a + 324a )x y(x) + (- 32a - 216a )x
+--R *
+--R +-+
+--R \|a
+--R +
+--R 3 2 3 3 2 2 4 3 2
+--R (32a + 216a )y(x) + (- 432a - 324a )x y(x) + (96a + 648a )x
y(x)
+--R +
+--R 4 3 3
+--R (- 144a - 108a )x
+--R *
+--R 2 +-+ 2
+--R x \|a
+--R (%e )
+--R Type: Expression
Integer
+--E 9
+
+--S 10 of 131
+ode103 := x*D(y(x),x) + x*y(x)**2 - (2*x**2+1)*y(x) - x**3
+--R
+--R , 2 2 3
+--R (10) xy (x) + x y(x) + (- 2x - 1)y(x) - x
+--R
+--R Type: Expression
Integer
+--E 10
+
+--S 11 of 131
+yx:=solve(ode103,y,x)
+--R
+--R +-+ +-+
+--R (2\|2 + 3)y(x) + x\|2 + x
+--R (11) -----------------------------------------
+--R 2 +-+
+--R +-+ +-+ x \|2
+--R ((6\|2 + 8)y(x) - 14x\|2 - 20x)%e
+--R Type: Union(Expression
Integer,...)
+--E 11
+
+--S 12 of 131
+ode103expr := x*D(yx,x) + x*yx**2 - (2*x**2+1)*yx - x**3
+--R
+--R (12)
+--R 2 +-+
+--R 2 +-+ 2 3 +-+ 3 x \|2 ,
+--R ((- 792x \|2 - 1120x )y(x) + 1912x \|2 + 2704x )%e y (x)
+--R
+--R +
+--R 3 +-+ 3 3 4 +-+ 4 2
+--R (- 792x \|2 - 1120x )y(x) + (5736x \|2 + 8112x )y(x)
+--R +
+--R 5 +-+ 5 6 +-+ 6
+--R (- 13848x \|2 - 19584x )y(x) + 11144x \|2 + 15760x
+--R *
+--R 2 +-+ 2
+--R x \|2
+--R (%e )
+--R +
+--R 2 +-+ 2 3
+--R ((- 1352x - 280)\|2 - 1912x - 396)y(x)
+--R +
+--R 3 +-+ 3 2
+--R ((5968x + 2028x)\|2 + 8440x + 2868x)y(x)
+--R +
+--R 4 2 +-+ 4 2
+--R ((- 5176x - 2984x )\|2 - 7320x - 4220x )y(x)
+--R +
+--R 5 3 +-+ 5 3
+--R (- 3264x - 676x )\|2 - 4616x - 956x
+--R *
+--R 2 +-+
+--R x \|2
+--R %e
+--R +
+--R +-+ 3 2 +-+ 2 2
+--R (99x\|2 + 140x)y(x) + (- 157x \|2 - 222x )y(x)
+--R +
+--R 3 +-+ 3 4 +-+ 4
+--R (- 181x \|2 - 256x )y(x) - 41x \|2 - 58x
+--R /
+--R +-+ 3 +-+ 2
+--R (792\|2 + 1120)y(x) + (- 5736x\|2 - 8112x)y(x)
+--R +
+--R 2 +-+ 2 3 +-+ 3
+--R (13848x \|2 + 19584x )y(x) - 11144x \|2 - 15760x
+--R *
+--R 2 +-+ 2
+--R x \|2
+--R (%e )
+--R Type: Expression
Integer
+--E 12
+
+--S 13 of 131
+ode104 := x*D(y(x),x) + a*x*y(x)**2 + 2*y(x) + b*x
+--R
+--R , 2
+--R (13) xy (x) + a x y(x) + 2y(x) + b x
+--R
+--R Type: Expression
Integer
+--E 13
+
+--S 14 of 131
+yx:=solve(ode104,y,x)
+--R
+--R +-----+ 2
+--R a x\|- a b + a x y(x) + a
+--R (14) ----------------------------------------------
+--R +-----+
+--R +-----+ 2x\|- a b
+--R ((2a x y(x) + 2)\|- a b + 2a b x)%e
+--R Type: Union(Expression
Integer,...)
+--E 14
+
+--S 15 of 131
+ode104expr := x*D(yx,x) + a*x*yx**2 + 2*yx + b*x
+--R
+--R (15)
+--R +-----+
+--R 3 4 2 3 +-----+ 3 2 4 2x\|- a b ,
+--R ((- 4a b x y(x) - 4a b x )\|- a b - 4a b x )%e y (x)
+--R
+--R +
+--R 3 2 4 3 2 2 3 2 2 3 4 2 2
+--R 4a b x y(x) + 12a b x y(x) + (- 12a b x + 12a b x )y(x)
+--R +
+--R 3 3 2
+--R - 12a b x + 4b x
+--R *
+--R +-----+
+--R \|- a b
+--R +
+--R 3 3 4 2 2 3 3 2 4 4 3 2
+--R 12a b x y(x) + 24a b x y(x) - 4a b x + 12a b x
+--R *
+--R +-----+ 2
+--R 2x\|- a b
+--R (%e )
+--R +
+--R 4 4 3 3 3 2 3 2 4 2 2
+--R - 4a b x y(x) - 16a b x y(x) + (- 4a b x - 16a b x )y(x)
+--R +
+--R 2 2 3
+--R - 8a b x - 4a b x
+--R *
+--R +-----+
+--R \|- a b
+--R +
+--R 4 3 3 4 2 4 3 2 2
+--R 4a b x y(x) + (- 4a b x + 12a b x )y(x)
+--R +
+--R 3 2 3 2 3 3 4 2 2 2
+--R (- 4a b x + 12a b x)y(x) - 4a b x + 4a b x + 4a b
+--R *
+--R +-----+
+--R 2x\|- a b
+--R %e
+--R +
+--R 5 4 3 4 3 2 4 4 3 2 3 3 2
+--R (- a x y(x) - 3a x y(x) + (- a b x - 3a x )y(x) - a b x - a x)
+--R *
+--R +-----+
+--R \|- a b
+--R +
+--R 5 4 2 4 3 4 2 4 3 2
+--R a b x y(x) + 2a b x y(x) + a b x + a b x
+--R /
+--R 3 3 3 2 2 2 2 2 3
+--R 4a b x y(x) + 12a b x y(x) + (- 12a b x + 12a b x)y(x)
+--R +
+--R 2 2
+--R - 12a b x + 4b
+--R *
+--R +-----+
+--R \|- a b
+--R +
+--R 3 2 3 2 2 2 2 2 3 3 2
+--R 12a b x y(x) + 24a b x y(x) - 4a b x + 12a b x
+--R *
+--R +-----+ 2
+--R 2x\|- a b
+--R (%e )
+--R Type: Expression
Integer
+--E 15
+
+--S 16 of 131
+ode105 := x*D(y(x),x) + a*x*y(x)**2 + b*y(x) + c*x + d
+--R
+--R , 2
+--R (16) xy (x) + a x y(x) + b y(x) + c x + d
+--R
+--R Type: Expression
Integer
+--E 16
+
+--S 17 of 131
+yx:=solve(ode105,y,x)
+--R WARNING (genufact): No known algorithm to factor
+--R 3 2 2 2
+--R ? - 3? + (- b + 2b + 2)? + b - 2b, trying square-free.
+--R
+--R (17) "failed"
+--R Type:
Union("failed",...)
+--E 17
+
+--S 18 of 131
+ode106 := x*D(y(x),x) + x**a*y(x)**2 + (a-b)*y(x)/2 + x**b
+--R
+--R , b 2 a
+--R 2xy (x) + 2x + 2y(x) x + (- b + a)y(x)
+--R
+--R (18) ----------------------------------------
+--R 2
+--R Type: Expression
Integer
+--E 18
+
+--S 19 of 131
+yx:=solve(ode106,y,x)
+--R
+--R (19) "failed"
+--R Type:
Union("failed",...)
+--E 19
+
+--S 20 of 131
+ode107 := x*D(y(x),x) + a*x**alpha*y(x)**2 + b*y(x) - c*x**beta
+--R
+--R , beta 2 alpha
+--R (20) xy (x) - c x + a y(x) x + b y(x)
+--R
+--R Type: Expression
Integer
+--E 20
+
+--S 21 of 131
+yx:=solve(ode107,y,x)
+--R
+--R (21) "failed"
+--R Type:
Union("failed",...)
+--E 21
+
+--S 22 of 131
+ode108 := x*D(y(x),x) - y(x)**2*log(x) + y(x)
+--R
+--R , 2
+--R (22) xy (x) - y(x) log(x) + y(x)
+--R
+--R Type: Expression
Integer
+--E 22
+
+--S 23 of 131
+yx:=solve(ode108,y,x)
+--R
+--R - y(x)log(x) - y(x) + 1
+--R (23) -----------------------
+--R x y(x)
+--R Type: Union(Expression
Integer,...)
+--E 23
+
+--S 24 of 131
+ode108expr := x*D(yx,x) - yx**2*log(x) + yx
+--R
+--R (24)
+--R 2 , 2 3 2 2
+--R - x y (x) - y(x) log(x) + (- 2y(x) + 2y(x))log(x)
+--R
+--R +
+--R 2 2
+--R (- y(x) + 2y(x) - 1)log(x) - x y(x)
+--R /
+--R 2 2
+--R x y(x)
+--R Type: Expression
Integer
+--E 24
+
+--S 25 of 131
+ode109 := x*D(y(x),x) - y(x)*(2*y(x)*log(x)-1)
+--R
+--R , 2
+--R (25) xy (x) - 2y(x) log(x) + y(x)
+--R
+--R Type: Expression
Integer
+--E 25
+
+--S 26 of 131
+yx:=solve(ode109,y,x)
+--R
+--R - 2y(x)log(x) - 2y(x) + 1
+--R (26) -------------------------
+--R x y(x)
+--R Type: Union(Expression
Integer,...)
+--E 26
+
+--S 27 of 131
+ode109expr := x*D(yx,x) - yx*(2*yx*log(x)-1)
+--R
+--R (27)
+--R 2 , 2 3 2 2
+--R - x y (x) - 8y(x) log(x) + (- 16y(x) + 8y(x))log(x)
+--R
+--R +
+--R 2 2
+--R (- 8y(x) + 8y(x) - 2)log(x) - 2x y(x)
+--R /
+--R 2 2
+--R x y(x)
+--R Type: Expression
Integer
+--E 27
+
+--S 28 of 131
+ode110 := x*D(y(x),x) + f(x)*(y(x)**2-x**2)
+--R
+--R , 2 2
+--R (28) xy (x) + f(x)y(x) - x f(x)
+--R
+--R Type: Expression
Integer
+--E 28
+
+--S 29 of 131
+yx:=solve(ode110,y,x)
+--R
+--R (29) "failed"
+--R Type:
Union("failed",...)
+--E 29
+
+--S 30 of 131
+ode111 := x*D(y(x),x) + y(x)**3 + 3*x*y(x)**2
+--R
+--R , 3 2
+--R (30) xy (x) + y(x) + 3x y(x)
+--R
+--R Type: Expression
Integer
+--E 30
+
+--S 31 of 131
+yx:=solve(ode111,y,x)
+--R
+--R (31) "failed"
+--R Type:
Union("failed",...)
+--E 31
+
+--S 32 of 131
+ode112 := x*D(y(x),x) - sqrt(y(x)**2 + x**2) - y(x)
+--R
+--R +----------+
+--R , | 2 2
+--R (32) xy (x) - \|y(x) + x - y(x)
+--R
+--R Type: Expression
Integer
+--E 32
+
+--S 33 of 131
+yx:=solve(ode112,y,x)
+--R
+--R (33) "failed"
+--R Type:
Union("failed",...)
+--E 33
+
+--S 34 of 131
+ode113 := x*D(y(x),x) + a*sqrt(y(x)**2 + x**2) - y(x)
+--R
+--R +----------+
+--R , | 2 2
+--R (34) xy (x) + a\|y(x) + x - y(x)
+--R
+--R Type: Expression
Integer
+--E 34
+
+--S 35 of 131
+yx:=solve(ode113,y,x)
+--R
+--R (35) "failed"
+--R Type:
Union("failed",...)
+--E 35
+
+--S 36 of 131
+ode114 := x*D(y(x),x) - x*sqrt(y(x)**2 + x**2) - y(x)
+--R
+--R +----------+
+--R , | 2 2
+--R (36) xy (x) - x\|y(x) + x - y(x)
+--R
+--R Type: Expression
Integer
+--E 36
+
+--S 37 of 131
+yx:=solve(ode114,y,x)
+--R
+--R (37) "failed"
+--R Type:
Union("failed",...)
+--E 37
+
+--S 38 of 131
+ode115 := x*D(y(x),x) - x*(y(x)-x)*sqrt(y(x)**2 + x**2) - y(x)
+--R
+--R +----------+
+--R , 2 | 2 2
+--R (38) xy (x) + (- x y(x) + x )\|y(x) + x - y(x)
+--R
+--R Type: Expression
Integer
+--E 38
+
+--S 39 of 131
+yx:=solve(ode115,y,x)
+--R
+--R (39) "failed"
+--R Type:
Union("failed",...)
+--E 39
+
+--S 40 of 131
+ode116 := x*D(y(x),x) - x*sqrt((y(x)**2 - x**2)*(y(x)**2-4*x**2)) - y(x)
+--R
+--R +----------------------+
+--R , | 4 2 2 4
+--R (40) xy (x) - x\|y(x) - 5x y(x) + 4x - y(x)
+--R
+--R Type: Expression
Integer
+--E 40
+
+--S 41 of 131
+yx:=solve(ode116,y,x)
+--R
+--R (41) "failed"
+--R Type:
Union("failed",...)
+--E 41
+
+--S 42 of 131
+ode117 := x*D(y(x),x) - x*exp(y(x)/x) - y(x) - x
+--R
+--R y(x)
+--R ----
+--R , x
+--R (42) xy (x) - x %e - y(x) - x
+--R
+--R Type: Expression
Integer
+--E 42
+
+--S 43 of 131
+yx:=solve(ode117,y,x)
+--R
+--R (43) "failed"
+--R Type:
Union("failed",...)
+--E 43
+
+--S 44 of 131
+ode118 := x*D(y(x),x) - y(x)*log(y(x))
+--R
+--R ,
+--R (44) xy (x) - y(x)log(y(x))
+--R
+--R Type: Expression
Integer
+--E 44
+
+--S 45 of 131
+yx:=solve(ode118,y,x)
+--R
+--R x
+--R (45) - ---------
+--R log(y(x))
+--R Type: Union(Expression
Integer,...)
+--E 45
+
+--S 46 of 131
+ode118expr := x*D(yx,x) - yx*log(yx)
+--R
+--R x 2 ,
+--R x y(x)log(y(x))log(- ---------) + x y (x) - x y(x)log(y(x))
+--R log(y(x))
+--R (46) -----------------------------------------------------------
+--R 2
+--R y(x)log(y(x))
+--R Type: Expression
Integer
+--E 46
+
+--S 47 of 131
+ode119 := x*D(y(x),x) - y(x)*(log(x*y(x))-1)
+--R
+--R ,
+--R (47) xy (x) - y(x)log(x y(x)) + y(x)
+--R
+--R Type: Expression
Integer
+--E 47
+
+--S 48 of 131
+yx:=solve(ode119,y,x)
+--R
+--R (48) "failed"
+--R Type:
Union("failed",...)
+--E 48
+
+--S 49 of 131
+ode120 := x*D(y(x),x) - y(x)*(x*log(x**2/y(x))+2)
+--R
+--R 2
+--R , x
+--R (49) xy (x) - x y(x)log(----) - 2y(x)
+--R y(x)
+--R Type: Expression
Integer
+--E 49
+
+--S 50 of 131
+yx:=solve(ode120,y,x)
+--R
+--R (50) "failed"
+--R Type:
Union("failed",...)
+--E 50
+
+--S 51 of 131
+ode121 := x*D(y(x),x) + sin(y(x)-x)
+--R
+--R ,
+--R (51) xy (x) + sin(y(x) - x)
+--R
+--R Type: Expression
Integer
+--E 51
+
+--S 52 of 131
+yx:=solve(ode121,y,x)
+--R
+--R (52) "failed"
+--R Type:
Union("failed",...)
+--E 52
+
+--S 53 of 131
+ode122 := x*D(y(x),x) + (sin(y(x))-3*x**2*cos(y(x)))*cos(y(x))
+--R
+--R , 2 2
+--R (53) xy (x) + cos(y(x))sin(y(x)) - 3x cos(y(x))
+--R
+--R Type: Expression
Integer
+--E 53
+
+--S 54 of 131
+yx:=solve(ode122,y,x)
+--R
+--R (54) "failed"
+--R Type:
Union("failed",...)
+--E 54
+
+--S 55 of 131
+ode123 := x*D(y(x),x) - x*sin(y(x)/x) - y(x)
+--R
+--R , y(x)
+--R (55) xy (x) - x sin(----) - y(x)
+--R x
+--R Type: Expression
Integer
+--E 55
+
+--S 56 of 131
+yx:=solve(ode123,y,x)
+--R
+--R (56) "failed"
+--R Type:
Union("failed",...)
+--E 56
+
+--S 57 of 131
+ode124 := x*D(y(x),x) + x*cos(y(x)/x) - y(x) + x
+--R
+--R , y(x)
+--R (57) xy (x) + x cos(----) - y(x) + x
+--R x
+--R Type: Expression
Integer
+--E 57
+
+--S 58 of 131
+yx:=solve(ode124,y,x)
+--R
+--R (58) "failed"
+--R Type:
Union("failed",...)
+--E 58
+
+--S 59 of 131
+ode125 := x*D(y(x),x) + x*tan(y(x)/x) - y(x)
+--R
+--R , y(x)
+--R (59) xy (x) + x tan(----) - y(x)
+--R x
+--R Type: Expression
Integer
+--E 59
+
+--S 60 of 131
+yx:=solve(ode125,y,x)
+--R
+--R (60) "failed"
+--R Type:
Union("failed",...)
+--E 60
+
+--S 61 of 131
+ode126 := x*D(y(x),x) - y(x)*f(x*y(x))
+--R
+--R ,
+--R (61) xy (x) - y(x)f(x y(x))
+--R
+--R Type: Expression
Integer
+--E 61
+
+--S 62 of 131
+yx:=solve(ode126,y,x)
+--R
+--R (62) "failed"
+--R Type:
Union("failed",...)
+--E 62
+
+--S 63 of 131
+ode127 := x*D(y(x),x) - y(x)*f(x**a*y(x)**b)
+--R
+--R a b ,
+--R (63) - y(x)f(x y(x) ) + xy (x)
+--R
+--R Type: Expression
Integer
+--E 63
+
+--S 64 of 131
+yx:=solve(ode127,y,x)
+--R
+--R (64) "failed"
+--R Type:
Union("failed",...)
+--E 64
+
+--S 65 of 131
+ode128 := x*D(y(x),x) + a*y(x) - f(x)*g(x**a*y(x))
+--R
+--R , a
+--R (65) xy (x) - f(x)g(y(x)x ) + a y(x)
+--R
+--R Type: Expression
Integer
+--E 65
+
+--S 66 of 131
+yx:=solve(ode128,y,x)
+--R
+--R (66) "failed"
+--R Type:
Union("failed",...)
+--E 66
+
+--S 67 of 131
+ode129 := (x+1)*D(y(x),x) + y(x)*(y(x)-x)
+--R
+--R , 2
+--R (67) (x + 1)y (x) + y(x) - x y(x)
+--R
+--R Type: Expression
Integer
+--E 67
+
+--S 68 of 131
+yx:=solve(ode129,y,x)
+--R
+--R x
+--R - x ++ 1
+--I (- x - 1)y(x)%e | ------------------------ d%BH + 1
+--I ++ 2 - %BH
+--I (%BH + 2%BH + 1)%e
+--R (68) ---------------------------------------------------------
+--R - x
+--R (x + 1)y(x)%e
+--R Type: Union(Expression
Integer,...)
+--E 68
+
+--S 69 of 131
+ode130 := 2*x*D(y(x),x) - y(x) -2*x**3
+--R
+--R , 3
+--R (69) 2xy (x) - y(x) - 2x
+--R
+--R Type: Expression
Integer
+--E 69
+
+--S 70 of 131
+ode130a:=solve(ode130,y,x)
+--R
+--R 3
+--R 2x +-+
+--R (70) [particular= ---,basis= [\|x ]]
+--R 5
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 70
+
+--S 71 of 131
+yx:=ode130a.particular
+--R
+--R 3
+--R 2x
+--R (71) ---
+--R 5
+--R Type: Expression
Integer
+--E 71
+
+--S 72 of 131
+ode130expr := 2*x*D(yx,x) - yx -2*x**3
+--R
+--R (72) 0
+--R Type: Expression
Integer
+--E 72
+
+--S 73 of 131
+ode131 := (2*x+1)*D(y(x),x) - 4*exp(-y(x)) + 2
+--R
+--R , - y(x)
+--R (73) (2x + 1)y (x) - 4%e + 2
+--R
+--R Type: Expression
Integer
+--E 73
+
+--S 74 of 131
+yx:=solve(ode131,y,x)
+--R
+--R - y(x) y(x)
+--R (74) (- 4x %e + 2x + 1)%e
+--R Type: Union(Expression
Integer,...)
+--E 74
+
+--S 75 of 131
+ode131expr := (2*x+1)*D(yx,x) - 4*exp(-yx) + 2
+--R
+--R (75)
+--R - y(x) y(x)
+--R (4x %e - 2x - 1)%e 2 y(x) ,
+--R - 4%e + (4x + 4x + 1)%e y (x)
+--R
+--R +
+--R - y(x) y(x)
+--R ((- 8x - 4)%e + 4x + 2)%e + 2
+--R Type: Expression
Integer
+--E 75
+
+--S 76 of 131
+ode132 := 3*x*D(y(x),x) - 3*x*log(x)*y(x)**4 - y(x)
+--R
+--R , 4
+--R (76) 3xy (x) - 3x y(x) log(x) - y(x)
+--R
+--R Type: Expression
Integer
+--E 76
+
+--S 77 of 131
+yx:=solve(ode132,y,x)
+--R
+--R 2 3 2 3
+--R - 6x y(x) log(x) + 3x y(x) - 4x
+--R (77) --------------------------------
+--R 3
+--R 4y(x)
+--R Type: Union(Expression
Integer,...)
+--E 77
+
+--S 78 of 131
+ode132expr := 3*x*D(yx,x) - 3*x*log(x)*yx**4 - yx
+--R
+--R (78)
+--R 2 8 , 9 12 5
+--R 2304x y(x) y (x) - 3888x y(x) log(x)
+--R
+--R +
+--R 9 12 8 9 4
+--R (7776x y(x) - 10368x y(x) )log(x)
+--R +
+--R 9 12 8 9 7 6 3
+--R (- 5832x y(x) + 15552x y(x) - 10368x y(x) )log(x)
+--R +
+--R 9 12 8 9 7 6 6 3 2
+--R (1944x y(x) - 7776x y(x) + 10368x y(x) - 4608x y(x) )log(x)
+--R +
+--R 9 2 12 8 9 7 6 6
3
+--R (- 243x - 1920x )y(x) + 1296x y(x) - 2592x y(x) + 2304x y(x)
+--R +
+--R 5
+--R - 768x
+--R *
+--R log(x)
+--R +
+--R 2 12 9
+--R - 192x y(x) - 512x y(x)
+--R /
+--R 12
+--R 256y(x)
+--R Type: Expression
Integer
+--E 78
+
+--S 79 of 131
+ode133 := x**2*D(y(x),x) + y(x) - x
+--R
+--R 2 ,
+--R (79) x y (x) + y(x) - x
+--R
+--R Type: Expression
Integer
+--E 79
+
+--S 80 of 131
+yx:=solve(ode133,y,x)
+--R
+--R 1 1
+--R - x -
+--R x ++ 1 x
+--I (80) [particular= %e | --------- d%BH ,basis= [%e ]]
+--R ++ 1
+--R ---
+--I %BH
+--I %BH %e
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 80
+
+--S 81 of 131
+ode134 := x**2*D(y(x),x) - y(x) + x**2*exp(x-1/x)
+--R
+--R 2
+--R x - 1
+--R ------
+--R 2 , 2 x
+--R (81) x y (x) + x %e - y(x)
+--R
+--R Type: Expression
Integer
+--E 81
+
+--S 82 of 131
+ode134a:=solve(ode134,y,x)
+--R
+--R 2
+--R x - 1 1
+--R ------ - -
+--R x x
+--R (82) [particular= - %e ,basis= [%e ]]
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 82
+
+--S 83 of 131
+yx:=ode134a.particular
+--R
+--R 2
+--R x - 1
+--R ------
+--R x
+--R (83) - %e
+--R Type: Expression
Integer
+--E 83
+
+--S 84 of 131
+ode134expr := x**2*D(yx,x) - yx + x**2*exp(x-1/x)
+--R
+--R (84) 0
+--R Type: Expression
Integer
+--E 84
+
+--S 85 of 131
+ode135 := x**2*D(y(x),x) - (x-1)*y(x)
+--R
+--R 2 ,
+--R (85) x y (x) + (- x + 1)y(x)
+--R
+--R Type: Expression
Integer
+--E 85
+
+--S 86 of 131
+ode135a:=solve(ode135,y,x)
+--R
+--R 1
+--R -
+--R x
+--R (86) [particular= 0,basis= [x %e ]]
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 86
+
+--S 87 of 131
+yx:=ode135a.particular
+--R
+--R (87) 0
+--R Type: Expression
Integer
+--E 87
+
+--S 88 of 131
+ode135expr := x**2*D(yx,x) - (x-1)*yx
+--R
+--R (88) 0
+--R Type: Expression
Integer
+--E 88
+
+--S 89 of 131
+ode136 := x**2*D(y(x),x) + y(x)**2 + x*y(x) + x**2
+--R
+--R 2 , 2 2
+--R (89) x y (x) + y(x) + x y(x) + x
+--R
+--R Type: Expression
Integer
+--E 89
+
+--S 90 of 131
+yx:=solve(ode136,y,x)
+--R
+--R (- y(x) - x)log(x) + x
+--R (90) ----------------------
+--R y(x) + x
+--R Type: Union(Expression
Integer,...)
+--E 90
+
+--S 91 of 131
+ode136expr := x**2*D(yx,x) + yx**2 + x*yx + x**2
+--R
+--R (91)
+--R 3 , 2 2 2
+--R - x y (x) + (y(x) + 2x y(x) + x )log(x)
+--R
+--R +
+--R 2 2 3 2 2 2 3
+--R (- x y(x) + (- 2x - 2x)y(x) - x - 2x )log(x) + (x - x)y(x) + 2x
y(x)
+--R +
+--R 4 2
+--R x + x
+--R /
+--R 2 2
+--R y(x) + 2x y(x) + x
+--R Type: Expression
Integer
+--E 91
+
+--S 92 of 131
+ode137 := x**2*D(y(x),x) - y(x)**2 - x*y(x)
+--R
+--R 2 , 2
+--R (92) x y (x) - y(x) - x y(x)
+--R
+--R Type: Expression
Integer
+--E 92
+
+--S 93 of 131
+yx:=solve(ode137,y,x)
+--R
+--R y(x)log(x) + x
+--R (93) --------------
+--R y(x)
+--R Type: Union(Expression
Integer,...)
+--E 93
+
+--S 94 of 131
+ode137expr := x**2*D(yx,x) - yx**2 - x*yx
+--R
+--R 3 , 2 2 2 2
2
+--R - x y (x) - y(x) log(x) + (- x y(x) - 2x y(x))log(x) + x y(x) -
x
+--R
+--R (94)
---------------------------------------------------------------------
+--R 2
+--R y(x)
+--R Type: Expression
Integer
+--E 94
+
+--S 95 of 131
+ode138 := x**2*D(y(x),x) - y(x)**2 - x*y(x) - x**2
+--R
+--R 2 , 2 2
+--R (95) x y (x) - y(x) - x y(x) - x
+--R
+--R Type: Expression
Integer
+--E 95
+
+--S 96 of 131
+yx:=solve(ode138,y,x)
+--R
+--R +---+ +---+
+--R (- 7\|- 1 + 9)y(x) + 9x\|- 1 + 7x
+--R (96) --------------------------------------------------------
+--R +---+
+--R +---+ +---+ - 2\|- 1 log(x)
+--R ((18\|- 1 + 14)y(x) - 14x\|- 1 + 18x)%e
+--R Type: Union(Expression
Integer,...)
+--E 96
+
+--S 97 of 131
+ode138expr := x**2*D(yx,x) - yx**2 - x*yx - x**2
+--R
+--R (97)
+--R 3 +---+ 3 4 +---+ 4
+--R ((- 1188x \|- 1 + 2716x )y(x) - 2716x \|- 1 - 1188x )
+--R *
+--R +---+
+--R - 2\|- 1 log(x) ,
+--R %e y (x)
+--R
+--R +
+--R 2 +---+ 2 3 3 +---+ 3 2
+--R (- 1188x \|- 1 + 2716x )y(x) + (- 8148x \|- 1 - 3564x )y(x)
+--R +
+--R 4 +---+ 4 5 +---+ 5
+--R (3564x \|- 1 - 8148x )y(x) + 2716x \|- 1 + 1188x
+--R *
+--R +---+ 2
+--R - 2\|- 1 log(x)
+--R (%e )
+--R +
+--R +---+ 3 2 +---+ 2 2
+--R (- 170x\|- 1 - 3310x)y(x) + (4498x \|- 1 - 2886x )y(x)
+--R +
+--R 3 +---+ 3 4 +---+ 4
+--R (2546x \|- 1 - 2122x )y(x) + 3310x \|- 1 - 170x
+--R *
+--R +---+
+--R - 2\|- 1 log(x)
+--R %e
+--R +
+--R +---+ 3 +---+ 2
+--R (297\|- 1 - 679)y(x) + (- 679x\|- 1 - 297x)y(x)
+--R +
+--R 2 +---+ 2 3 +---+ 3
+--R (297x \|- 1 - 679x )y(x) - 679x \|- 1 - 297x
+--R /
+--R +---+ 3 +---+ 2
+--R (1188\|- 1 - 2716)y(x) + (8148x\|- 1 + 3564x)y(x)
+--R +
+--R 2 +---+ 2 3 +---+ 3
+--R (- 3564x \|- 1 + 8148x )y(x) - 2716x \|- 1 - 1188x
+--R *
+--R +---+ 2
+--R - 2\|- 1 log(x)
+--R (%e )
+--R Type: Expression
Integer
+--E 97
+
+--S 98 of 131
+ode139 := x**2*(D(y(x),x)+y(x)**2) + a*x**k - b*(b-1)
+--R
+--R 2 , k 2 2 2
+--R (98) x y (x) + a x + x y(x) - b + b
+--R
+--R Type: Expression
Integer
+--E 98
+
+--S 99 of 131
+yx:=solve(ode139,y,x)
+--R
+--R (99) "failed"
+--R Type:
Union("failed",...)
+--E 99
+
+--S 100 of 131
+ode140 := x**2*(D(y(x),x)+y(x)**2) + 4*x*y(x) + 2
+--R
+--R 2 , 2 2
+--R (100) x y (x) + x y(x) + 4x y(x) + 2
+--R
+--R Type: Expression
Integer
+--E 100
+
+--S 101 of 131
+yx:=solve(ode140,y,x)
+--R
+--R x y(x) + 2
+--R (101) --------------------
+--R 2
+--R (x - x)y(x) + x - 2
+--R Type: Union(Expression
Integer,...)
+--E 101
+
+--S 102 of 131
+ode140expr := x**2*(D(yx,x)+yx**2) + 4*x*yx + 2
+--R
+--R (102)
+--R 4 , 4 3 2 2 3 2 2
+--R - x y (x) + (6x - 8x + 2x )y(x) + (16x - 28x + 8x)y(x) + 12x - 24x
+ 8
+--R
+--R
----------------------------------------------------------------------------
+--R 4 3 2 2 3 2 2
+--R (x - 2x + x )y(x) + (2x - 6x + 4x)y(x) + x - 4x + 4
+--R Type: Expression
Integer
+--E 102
+
+--S 103 of 131
+ode141 := x**2*(D(y(x),x)+y(x)**2) + a*x*y(x) + b
+--R
+--R 2 , 2 2
+--R (103) x y (x) + x y(x) + a x y(x) + b
+--R
+--R Type: Expression
Integer
+--E 103
+
+--S 104 of 131
+yx:=solve(ode141,y,x)
+--R 2
+--R WARNING (genufact): No known algorithm to factor ? + (a - 1)? + b
+--R , trying square-free.
+--R
+--R (104)
+--R +------------------+
+--R | 2
+--R \|- 4b + a - 2a + 1 - 2x y(x) - a + 1
+--R /
+--R +------------------+
+--R | 2 2
+--R ((2x y(x) + a - 1)\|- 4b + a - 2a + 1 - 4b + a - 2a + 1)
+--R *
+--R +------------------+
+--R | 2
+--R - log(x)\|- 4b + a - 2a + 1
+--R %e
+--R Type: Union(Expression
Integer,...)
+--E 104
+
+--S 105 of 131
+ode141expr := x**2*(D(yx,x)+yx**2) + a*x*yx + b
+--R
+--R (105)
+--R 2 4 3 2
3
+--R ((- 8b + 2a - 4a + 2)x y(x) + ((- 4a + 4)b + a - 3a + 3a -
1)x )
+--R *
+--R +------------------+
+--R | 2
+--R \|- 4b + a - 2a + 1
+--R +
+--R 2 2 4 3 2 3
+--R (16b + (- 8a + 16a - 8)b + a - 4a + 6a - 4a + 1)x
+--R *
+--R +------------------+
+--R | 2
+--R - log(x)\|- 4b + a - 2a + 1 ,
+--R %e y (x)
+--R
+--R +
+--R 2 2 3 3
+--R (8b + (- 2a + 4a - 2)b)x y(x)
+--R +
+--R 2 3 2 2 2
+--R ((12a - 12)b + (- 3a + 9a - 9a + 3)b)x y(x)
+--R +
+--R 3 2 2
+--R - 24b + (18a - 36a + 18)b
+--R +
+--R 4 3 2
+--R (- 3a + 12a - 18a + 12a - 3)b
+--R *
+--R x y(x)
+--R +
+--R 3 3 2 2
+--R (- 12a + 12)b + (7a - 21a + 21a - 7)b
+--R +
+--R 5 4 3 2
+--R (- a + 5a - 10a + 10a - 5a + 1)b
+--R *
+--R +------------------+
+--R | 2
+--R \|- 4b + a - 2a + 1
+--R +
+--R 3 2 2 4 3 2
2
+--R (- 48b + (24a - 48a + 24)b + (- 3a + 12a - 18a + 12a -
3)b)x
+--R *
+--R 2
+--R y(x)
+--R +
+--R 3 3 2 2
+--R (- 48a + 48)b + (24a - 72a + 72a - 24)b
+--R +
+--R 5 4 3 2
+--R (- 3a + 15a - 30a + 30a - 15a + 3)b
+--R *
+--R x y(x)
+--R +
+--R 4 2 3 4 3 2 2
+--R 16b + (- 24a + 48a - 24)b + (9a - 36a + 54a - 36a + 9)b
+--R +
+--R 6 5 4 3 2
+--R (- a + 6a - 15a + 20a - 15a + 6a - 1)b
+--R *
+--R +------------------+ 2
+--R | 2
+--R - log(x)\|- 4b + a - 2a + 1
+--R (%e )
+--R +
+--R 2 4 3
+--R (- 8b + 2a - 4a + 2)x y(x)
+--R +
+--R 3 2 3 2
+--R ((- 16a + 4)b + 4a - 9a + 6a - 1)x y(x)
+--R +
+--R 2 2 4 3 2 2
+--R (- 8b + (- 6a + 4a + 2)b + 2a - 6a + 6a - 2a)x y(x)
+--R +
+--R 2 3 2
+--R ((- 8a + 4)b + (2a - 5a + 4a - 1)b)x
+--R *
+--R +------------------+
+--R | 2
+--R \|- 4b + a - 2a + 1
+--R +
+--R 3 2 4 3
+--R (- 8a b + 2a - 4a + 2a)x y(x)
+--R +
+--R 2 2 4 3 2 3 2
+--R (16b + (- 20a + 28a - 8)b + 4a - 13a + 15a - 7a + 1)x y(x)
+--R +
+--R 2 3 2 5 4 3 2 2
+--R (8a b + (- 10a + 20a - 10a)b + 2a - 8a + 12a - 8a + 2a)x
y(x)
+--R +
+--R 3 2 2 4 3 2
+--R (16b + (- 12a + 20a - 8)b + (2a - 7a + 9a - 5a + 1)b)x
+--R *
+--R +------------------+
+--R | 2
+--R - log(x)\|- 4b + a - 2a + 1
+--R %e
+--R +
+--R 5 3 4 2 2 3
+--R - 2x y(x) + (- 3a + 3)x y(x) + (- 2b - a + 2a - 1)x y(x)
+--R +
+--R 2
+--R (- a + 1)b x
+--R *
+--R +------------------+
+--R | 2
+--R \|- 4b + a - 2a + 1
+--R +
+--R 2 4 2 3 2 3
+--R (- 4b + a - 2a + 1)x y(x) + ((- 4a + 4)b + a - 3a + 3a - 1)x y(x)
+--R +
+--R 2 2 2
+--R (- 4b + (a - 2a + 1)b)x
+--R /
+--R 2 3 3
+--R (8b - 2a + 4a - 2)x y(x)
+--R +
+--R 3 2 2 2
+--R ((12a - 12)b - 3a + 9a - 9a + 3)x y(x)
+--R +
+--R 2 2 4 3 2
+--R (- 24b + (18a - 36a + 18)b - 3a + 12a - 18a + 12a - 3)x
y(x)
+--R +
+--R 2 3 2 5 4 3
2
+--R (- 12a + 12)b + (7a - 21a + 21a - 7)b - a + 5a - 10a +
10a
+--R +
+--R - 5a + 1
+--R *
+--R +------------------+
+--R | 2
+--R \|- 4b + a - 2a + 1
+--R +
+--R 2 2 4 3 2 2 2
+--R (- 48b + (24a - 48a + 24)b - 3a + 12a - 18a + 12a - 3)x y(x)
+--R +
+--R 2 3 2 5 4 3
+--R (- 48a + 48)b + (24a - 72a + 72a - 24)b - 3a + 15a - 30a
+--R +
+--R 2
+--R 30a - 15a + 3
+--R *
+--R x y(x)
+--R +
+--R 3 2 2 4 3 2 6
+--R 16b + (- 24a + 48a - 24)b + (9a - 36a + 54a - 36a + 9)b - a
+--R +
+--R 5 4 3 2
+--R 6a - 15a + 20a - 15a + 6a - 1
+--R *
+--R +------------------+ 2
+--R | 2
+--R - log(x)\|- 4b + a - 2a + 1
+--R (%e )
+--R Type: Expression
Integer
+--E 105
+
+--S 106 of 131
+ode142 := x**2*(D(y(x),x)-y(x)**2) - a*x**2*y(x) + a*x + 2
+--R
+--R 2 , 2 2 2
+--R (106) x y (x) - x y(x) - a x y(x) + a x + 2
+--R
+--R Type: Expression
Integer
+--E 106
+
+--S 107 of 131
+yx:=solve(ode142,y,x)
+--R
+--R 2 3 2 3 3 2 2
+--R (a x - 2a x + 2x)y(x) + a x - a x + 2a x - 2
+--R (107) ------------------------------------------------
+--R 3 3 - a x
+--R (a x y(x) - a )%e
+--R Type: Union(Expression
Integer,...)
+--E 107
+
+--S 108 of 131
+ode142expr := x**2*(D(yx,x)-yx**2) - a*x**2*yx + a*x + 2
+--R
+--R (108)
+--R 6 6 - a x ,
+--R - a x %e y (x)
+--R
+--R +
+--R 7 3 6 2 2 7 2 6 7 6 - a x 2
+--R ((a x + 2a x )y(x) + (- 2a x - 4a x)y(x) + a x + 2a )(%e )
+--R +
+--R 5 5 4 4 2 6 5 5 4 4 3 6 4 5
3
+--R (2a x - 2a x )y(x) + (2a x - 4a x + 4a x )y(x) - 3a x + 2a x
+--R +
+--R 4 2
+--R - 2a x
+--R *
+--R - a x
+--R %e
+--R +
+--R 4 8 3 7 2 6 5 4 2
+--R (- a x + 4a x - 8a x + 8a x - 4x )y(x)
+--R +
+--R 5 8 4 7 3 6 2 5 4 3 6 8 5 7
+--R (- 2a x + 6a x - 12a x + 16a x - 16a x + 8x )y(x) - a x + 2a x
+--R +
+--R 4 6 3 5 2 4 3 2
+--R - 5a x + 8a x - 8a x + 8a x - 4x
+--R /
+--R 6 2 2 6 6 - a x 2
+--R (a x y(x) - 2a x y(x) + a )(%e )
+--R Type: Expression
Integer
+--E 108
+
+--S 109 of 131
+ode143 := x**2*(D(y(x),x)+a*y(x)**2) - b
+--R
+--R 2 , 2 2
+--R (109) x y (x) + a x y(x) - b
+--R
+--R Type: Expression
Integer
+--E 109
+
+--S 110 of 131
+yx:=solve(ode143,y,x)
+--R 2
+--R WARNING (genufact): No known algorithm to factor ? - ? - a b
+--R , trying square-free.
+--R
+--R +--------+ 2
+--R a\|4a b + 1 - 2a x y(x) + a
+--R (110) ------------------------------------------------------------
+--R +--------+
+--R +--------+ - log(x)\|4a b + 1
+--R ((2a x y(x) - 1)\|4a b + 1 + 4a b + 1)%e
+--R Type: Union(Expression
Integer,...)
+--E 110
+
+--S 111 of 131
+ode143expr := x**2*(D(yx,x)+a*yx**2) - b
+--R
+--R (111)
+--R +--------+
+--R 3 2 3 - log(x)\|4a b + 1 ,
+--R (- 8a b - 2a )x %e y (x)
+--R
+--R +
+--R 2 2 2 +--------+
+--R ((- 8a b - 2a b)x y(x) + 4a b + b)\|4a b + 1
+--R +
+--R 3 2 2 2 2 2 2 2 3 2
+--R (- 8a b - 2a b)x y(x) + (8a b + 2a b)x y(x) - 8a b - 6a b -
b
+--R *
+--R +--------+ 2
+--R - log(x)\|4a b + 1
+--R (%e )
+--R +
+--R +--------+
+--R 4 3 3 2 3 2 2 - log(x)\|4a b + 1
+--R ((- 8a b - 2a )x y(x) + (8a b + 2a b)x)%e
+--R +
+--R 4 3 3 2 +--------+ 5 4 2 4 3 4
3 2
+--R (- 2a x y(x) + a x )\|4a b + 1 + 2a x y(x) - 2a x y(x) + (2a b + a
)x
+--R /
+--R 2 +--------+ 3 2 2 2
+--R ((8a b + 2a)x y(x) - 4a b - 1)\|4a b + 1 + (8a b + 2a )x y(x)
+--R +
+--R 2 2 2
+--R (- 8a b - 2a)x y(x) + 8a b + 6a b + 1
+--R *
+--R +--------+ 2
+--R - log(x)\|4a b + 1
+--R (%e )
+--R Type: Expression
Integer
+--E 111
+
+--S 112 of 131
+ode144 := x**2*(D(y(x),x)+a*y(x)**2) + b*x**alpha + c
+--R
+--R 2 , alpha 2 2
+--R (112) x y (x) + b x + a x y(x) + c
+--R
+--R Type: Expression
Integer
+--E 112
+
+--S 113 of 131
+yx:=solve(ode144,y,x)
+--R
+--R (113) "failed"
+--R Type:
Union("failed",...)
+--E 113
+
+--S 114 of 131
+ode145 := x**2*D(y(x),x) + a*y(x)**3 - a*x**2*y(x)**2
+--R
+--R 2 , 3 2 2
+--R (114) x y (x) + a y(x) - a x y(x)
+--R
+--R Type: Expression
Integer
+--E 114
+
+--S 115 of 131
+yx:=solve(ode145,y,x)
+--R
+--R (115) "failed"
+--R Type:
Union("failed",...)
+--E 115
+
+--S 116 of 131
+ode146 := x**2*D(y(x),x) + x*y(x)**3 + a*y(x)**2
+--R
+--R 2 , 3 2
+--R (116) x y (x) + x y(x) + a y(x)
+--R
+--R Type: Expression
Integer
+--E 116
+
+--S 117 of 131
+yx:=solve(ode146,y,x)
+--R
+--R (117) "failed"
+--R Type:
Union("failed",...)
+--E 117
+
+--S 118 of 131
+ode147 := x**2*D(y(x),x) + a*x**2*y(x)**3 + b*y(x)**2
+--R
+--R 2 , 2 3 2
+--R (118) x y (x) + a x y(x) + b y(x)
+--R
+--R Type: Expression
Integer
+--E 118
+
+--S 119 of 131
+yx:=solve(ode147,y,x)
+--R
+--R (119) "failed"
+--R Type:
Union("failed",...)
+--E 119
+
+--S 120 of 131
+ode148 := (x**2+1)*D(y(x),x) + x*y(x) - 1
+--R
+--R 2 ,
+--R (120) (x + 1)y (x) + x y(x) - 1
+--R
+--R Type: Expression
Integer
+--E 120
+
+--S 121 of 131
+ode148a:=solve(ode148,y,x)
+--R
+--R +------+
+--R | 2
+--R log(\|x + 1 - x) 1
+--R (121) [particular= - ------------------,basis= [---------]]
+--R +------+ +------+
+--R | 2 | 2
+--R \|x + 1 \|x + 1
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 121
+
+--S 122 of 131
+yx:=ode148a.particular
+--R
+--R +------+
+--R | 2
+--R log(\|x + 1 - x)
+--R (122) - ------------------
+--R +------+
+--R | 2
+--R \|x + 1
+--R Type: Expression
Integer
+--E 122
+
+--S 123 of 131
+ode148expr := (x**2+1)*D(yx,x) + x*yx - 1
+--R
+--R (123) 0
+--R Type: Expression
Integer
+--E 123
+
+--S 124 of 131
+ode149 := (x**2+1)*D(y(x),x) + x*y(x) - x*(x**2+1)
+--R
+--R 2 , 3
+--R (124) (x + 1)y (x) + x y(x) - x - x
+--R
+--R Type: Expression
Integer
+--E 124
+
+--S 125 of 131
+ode149a:=solve(ode149,y,x)
+--R
+--R 2
+--R x + 1 1
+--R (125) [particular= ------,basis= [---------]]
+--R 3 +------+
+--R | 2
+--R \|x + 1
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 125
+
+--S 126 of 131
+yx:=ode149a.particular
+--R
+--R 2
+--R x + 1
+--R (126) ------
+--R 3
+--R Type: Expression
Integer
+--E 126
+
+--S 127 of 131
+ode149expr := (x**2+1)*D(yx,x) + x*yx - x*(x**2+1)
+--R
+--R (127) 0
+--R Type: Expression
Integer
+--E 127
+
+--S 128 of 131
+ode150 := (x**2+1)*D(y(x),x) + 2*x*y(x) - 2*x**2
+--R
+--R 2 , 2
+--R (128) (x + 1)y (x) + 2x y(x) - 2x
+--R
+--R Type: Expression
Integer
+--E 128
+
+--S 129 of 131
+ode150a:=solve(ode150,y,x)
+--R
+--R 3
+--R 2x + 3 1
+--R (129) [particular= -------,basis= [------]]
+--R 2 2
+--R 3x + 3 x + 1
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 129
+
+--S 130 of 131
+yx:=ode150a.particular
+--R
+--R 3
+--R 2x + 3
+--R (130) -------
+--R 2
+--R 3x + 3
+--R Type: Expression
Integer
+--E 130
+
+--S 131 of 131
+ode150expr := (x**2+1)*D(yx,x) + 2*x*yx - 2*x**2
+--R
+--R (131) 0
+--R Type: Expression
Integer
+--E 131
+)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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