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[Axiom-developer] 20071004.01.tpd.patch
From: |
daly |
Subject: |
[Axiom-developer] 20071004.01.tpd.patch |
Date: |
Thu, 4 Oct 2007 10:12:20 -0500 |
This patch adds regression testing of Axiom's ordinary differential
equation facilities using the first 50 equations from the Kamke test suite.
==========================================================================
diff --git a/changelog b/changelog
index 21958ab..46dc9dc 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20071004 tpd src/input/Makefile kamke0.input regression test added
+20071004 tpd src/input/kamke0.input ODE regression test added
20071001 tpd src/algebra/exposed.lisp add (|AxiomServer| . AXSERV) to basic
20071001 tpd src/algebra/Makefile add axserver.spad
20071001 acr src/algebra/axserver.spad axserver socket connection code
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index f62095a..c1ade3e 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -322,6 +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 \
kernel.regress knot2.regress kovacic.regress kuipers.regress \
laplace.regress leg.regress limit.regress lindep.regress \
list.regress lode.regress lodesys.regress lodo1.regress \
@@ -556,11 +557,12 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input
${OUT}/algfacob.input \
${OUT}/images3.input ${OUT}/images6.input ${OUT}/images6a.input \
${OUT}/images7.input ${OUT}/images7a.input ${OUT}/infprod.input \
${OUT}/intaf.input ${OUT}/intbypart.input \
- ${OUT}/intdeq.input ${OUT}/intef.input \
+ ${OUT}/intdeq.input ${OUT}/intef.input \
${OUT}/intg0.input ${OUT}/intheory.input ${OUT}/int.input \
${OUT}/intlf.input ${OUT}/intmix.input ${OUT}/intrf.input \
${OUT}/ipftest.input ${OUT}/is.input ${OUT}/isprime.input \
- ${OUT}/kafile.input ${OUT}/kernel.input ${OUT}/knot.input \
+ ${OUT}/kafile.input ${OUT}/kamke0.input \
+ ${OUT}/kernel.input ${OUT}/knot.input \
${OUT}/kovacic.input ${OUT}/kuipers.input \
${OUT}/laplace.input ${OUT}/leg.input ${OUT}/lexp.input \
${OUT}/lextripk.input ${OUT}/lib.input ${OUT}/limit.input \
@@ -825,6 +827,7 @@ DOCFILES= \
${DOC}/intmix.input.dvi ${DOC}/intrf.input.dvi \
${DOC}/ipftest.input.dvi ${DOC}/is.input.dvi \
${DOC}/isprime.input.dvi ${DOC}/kafile.input.dvi \
+ ${DOC}/kamke0.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/kamke0.input.pamphlet b/src/input/kamke0.input.pamphlet
new file mode 100644
index 0000000..d1a9d8b
--- /dev/null
+++ b/src/input/kamke0.input.pamphlet
@@ -0,0 +1,1904 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input kamke0.input}
+\author{Timothy Daly}
+\maketitle
+\begin{abstract}
+This is the first 50 of the Kamke test suite as published by
+E. S. Cheb-Terrab\cite{1}. They have been rewritten using Axiom
+syntax. Where possible we show that the particular solution actually
+satisfies the original ordinary differential equation.
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+<<*>>=
+)spool kamke0.output
+)set break resume
+)set mes auto off
+)clear all
+
+--S 1 of 134
+y:=operator 'y
+--R
+--R
+--R (1) y
+--R Type:
BasicOperator
+--E 1
+
+--S 2 of 134
+f := operator 'f
+--R
+--R (2) f
+--R Type:
BasicOperator
+--E 2
+
+--S 3 of 134
+g := operator 'g
+--R
+--R (3) g
+--R Type:
BasicOperator
+--E 3
+
+--S 4 of 134
+ode1 := D(y(x),x) - (a4*x**4+a3*x**3+a2*x**2+a1*x+a0)**(-1/2)
+--R
+--R
+--R +---------------------------------+
+--R | 4 3 2 ,
+--R \|a4 x + a3 x + a2 x + a1 x + a0 y (x) - 1
+--R
+--R (4) ---------------------------------------------
+--R +---------------------------------+
+--R | 4 3 2
+--R \|a4 x + a3 x + a2 x + a1 x + a0
+--R Type: Expression
Integer
+--E 4
+
+--S 5 of 134
+ode1a:=solve(ode1,y,x)
+--R
+--R
+--R (5)
+--R x
+--R ++ 1
+--I [particular= | ------------------------------------- d%N ,basis= [1]]
+--R ++ +----------------------------------+
+--R | 4 3 2
+--I \|%N a4 + %N a3 + %N a2 + %N a1 + a0
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 5
+
+--S 6 of 134
+ode2 := D(y(x),x) + a*y(x) - c*exp(b*x)
+--R
+--R
+--R , b x
+--R (6) y (x) - c %e + a y(x)
+--R
+--R Type: Expression
Integer
+--E 6
+
+--S 7 of 134
+ode2a:=solve(ode2,y,x)
+--R
+--R
+--R b x
+--R c %e - a x
+--R (7) [particular= -------,basis= [%e ]]
+--R b + a
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 7
+
+--S 8 of 134
+yx:=ode2a.particular
+--R
+--R b x
+--R c %e
+--R (8) -------
+--R b + a
+--R Type: Expression
Integer
+--E 8
+
+--S 9 of 134
+ode2expr:=D(yx,x) + a*yx -c*exp(b*x)
+--R
+--R (9) 0
+--R Type: Expression
Integer
+--E 9
+
+--S 10 of 134
+ode3 := D(y(x),x) + a*y(x) - b*sin(c*x)
+--R
+--R ,
+--R (10) y (x) - b sin(c x) + a y(x)
+--R
+--R Type: Expression
Integer
+--E 10
+
+--S 11 of 134
+ode3a:=solve(ode3,y,x)
+--R
+--R a b sin(c x) - b c cos(c x) - a x
+--R (11) [particular= ---------------------------,basis= [%e ]]
+--R 2 2
+--R c + a
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 11
+
+--S 12 of 134
+yx:=ode3a.particular
+--R
+--R a b sin(c x) - b c cos(c x)
+--R (12) ---------------------------
+--R 2 2
+--R c + a
+--R Type: Expression
Integer
+--E 12
+
+--S 13 of 134
+ode3expr:=D(yx,x) + a*yx - b*sin(c*x)
+--R
+--R (13) 0
+--R Type: Expression
Integer
+--E 13
+
+--S 14 of 134
+ode4 := D(y(x),x) + 2*x*y(x) - x*exp(-x**2)
+--R
+--R 2
+--R , - x
+--R (14) y (x) - x %e + 2x y(x)
+--R
+--R Type: Expression
Integer
+--E 14
+
+--S 15 of 134
+ode4a:=solve(ode4,y,x)
+--R
+--R 2
+--R 2 - x 2
+--R x %e - x
+--R (15) [particular= --------,basis= [%e ]]
+--R 2
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 15
+
+--S 16 of 134
+yx:=ode4a.particular
+--R
+--R 2
+--R 2 - x
+--R x %e
+--R (16) --------
+--R 2
+--R Type: Expression
Integer
+--E 16
+
+--S 17 of 134
+ode4expr:=D(yx,x) + 2*x*yx - x*exp(-x**2)
+--R
+--R (17) 0
+--R Type: Expression
Integer
+--E 17
+
+--S 18 of 134
+ode5 := D(y(x),x) + y(x)*cos(x) - exp(2*x)
+--R
+--R , 2x
+--R (18) y (x) - %e + y(x)cos(x)
+--R
+--R Type: Expression
Integer
+--E 18
+
+--S 19 of 134
+ode5a:=solve(ode5,y,x)
+--R
+--I x 2%H
+--R - sin(x) ++ %e - sin(x)
+--I (19) [particular= %e | ----------- d%H ,basis= [%e ]]
+--I ++ - sin(%H)
+--R %e
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 19
+
+--S 20 of 134
+ode6 := D(y(x),x) + y(x)*cos(x) - sin(2*x)/2
+--R
+--R ,
+--R 2y (x) - sin(2x) + 2y(x)cos(x)
+--R
+--R (20) ------------------------------
+--R 2
+--R Type: Expression
Integer
+--E 20
+
+--S 21 of 134
+ode6a:=solve(ode6,y,x)
+--R
+--R - sin(x)
+--R (21) [particular= sin(x) - 1,basis= [%e ]]
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 21
+
+--S 22 of 134
+yx:=ode6a.particular
+--R
+--R (22) sin(x) - 1
+--R Type: Expression
Integer
+--E 22
+
+--S 23 of 134
+ode6expr:=D(yx,x) + yx*cos(x) - sin(2*x)/2
+--R
+--R - sin(2x) + 2cos(x)sin(x)
+--R (23) -------------------------
+--R 2
+--R Type: Expression
Integer
+--E 23
+
+--S 24 of 134
+sin2rule := rule 2*cos(x)*sin(x) == sin(2*x)
+--R
+--I (24) 2%Y cos(x)sin(x) == %Y sin(2x)
+--R Type: RewriteRule(Integer,Integer,Expression
Integer)
+--E 24
+
+--S 25 of 134
+sin2rule ode6expr
+--R
+--R (25) 0
+--R Type: Expression
Integer
+--E 25
+
+--S 26 of 134
+ode7 := D(y(x),x) + y(x)*cos(x) - exp(-sin(x))
+--R
+--R , - sin(x)
+--R (26) y (x) - %e + y(x)cos(x)
+--R
+--R Type: Expression
Integer
+--E 26
+
+--S 27 of 134
+ode7a:=solve(ode7,y,x)
+--R
+--R - sin(x) - sin(x)
+--R (27) [particular= x %e ,basis= [%e ]]
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 27
+
+--S 28 of 134
+yx:=ode7a.particular
+--R
+--R - sin(x)
+--R (28) x %e
+--R Type: Expression
Integer
+--E 28
+
+--S 29 of 134
+ode7expr := D(yx,x) + yx*cos(x) - exp(-sin(x))
+--R
+--R (29) 0
+--R Type: Expression
Integer
+--E 29
+
+--S 30 of 134
+ode8 := D(y(x),x) + y(x)*tan(x) - sin(2*x)
+--R
+--R ,
+--R (30) y (x) + y(x)tan(x) - sin(2x)
+--R
+--R Type: Expression
Integer
+--E 30
+
+--S 31 of 134
+ode8a:=solve(ode8,y,x)
+--R
+--R (31)
+--R +-------+
+--R 2 | 1
+--R (- 2cos(x) + 2cos(x)) |-------
+--R 4| 4
+--R \|cos(x) 1
+--R [particular= --------------------------------,basis= [--------------]]
+--R +-----------+ +-----------+
+--R | 2 | 2
+--R \|tan(x) + 1 \|tan(x) + 1
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 31
+
+--S 32 of 134
+yx:=ode8a.particular
+--R
+--R +-------+
+--R 2 | 1
+--R (- 2cos(x) + 2cos(x)) |-------
+--R 4| 4
+--R \|cos(x)
+--R (32) --------------------------------
+--R +-----------+
+--R | 2
+--R \|tan(x) + 1
+--R Type: Expression
Integer
+--E 32
+
+--S 33 of 134
+ode8expr:=D(yx,x) + yx*tan(x) - sin(2*x)
+--R
+--R +-------+3 +-----------+
+--R 3 | 1 | 2
+--R - cos(x) sin(2x) |------- \|tan(x) + 1 + 2sin(x)
+--R 4| 4
+--R \|cos(x)
+--R (33) ---------------------------------------------------
+--R +-------+3 +-----------+
+--R 3 | 1 | 2
+--R cos(x) |------- \|tan(x) + 1
+--R 4| 4
+--R \|cos(x)
+--R Type: Expression
Integer
+--E 33
+
+--S 34 of 134
+ode9 := D(y(x),x) - (sin(log(x)) + cos(log(x)) +a)*y(x)
+--R
+--R ,
+--R (34) y (x) - y(x)sin(log(x)) - y(x)cos(log(x)) - a y(x)
+--R
+--R Type: Expression
Integer
+--E 34
+
+--S 35 of 134
+ode9a:=solve(ode9,y,x)
+--R
+--R x sin(log(x)) + a x
+--R (35) [particular= 0,basis= [%e ]]
+--RType: Union(Record(particular: Expression Integer,basis: List Expression
Integer),...)
+--E 35
+
+--S 36 of 134
+yx:=ode9a.particular
+--R
+--R (36) 0
+--R Type: Expression
Integer
+--E 36
+
+--S 37 of 134
+ode9expr:=D(yx,x) - (sin(log(x)) + cos(log(x)) +a)*yx
+--R
+--R (37) 0
+--R Type: Expression
Integer
+--E 37
+
+--S 38 of 134
+ode10 := D(y(x),x) + D(f(x),x)*y(x) - f(x)*D(f(x),x)
+--R
+--R , ,
+--R (38) y (x) + (y(x) - f(x))f (x)
+--R
+--R Type: Expression
Integer
+--E 38
+
+--S 39 of 134
+ode10a:=solve(ode10,y,x)
+--R
+--R
+--R >> Error detected within library code:
+--R Function not supported by Risch d.e.
+--R
+--R Continuing to read the file...
+--R
+--E 39
+
+--S 40 of 134
+ode11 := D(y(x),x) + f(x)*y(x) - g(x)
+--R
+--R ,
+--R (39) y (x) + f(x)y(x) - g(x)
+--R
+--R Type: Expression
Integer
+--E 40
+
+--S 41 of 134
+ode11a:=solve(ode11,y,x)
+--R
+--R
+--R >> Error detected within library code:
+--R Function not supported by Risch d.e.
+--R
+--R Continuing to read the file...
+--R
+--E 41
+
+--S 42 of 134
+ode12 := D(y(x),x) + y(x)**2 - 1
+--R
+--R , 2
+--R (40) y (x) + y(x) - 1
+--R
+--R Type: Expression
Integer
+--E 42
+
+--S 43 of 134
+yx:=solve(ode12,y,x)
+--R
+--R - log(y(x) + 1) + log(y(x) - 1) + 2x
+--R (41) ------------------------------------
+--R 2
+--R Type: Union(Expression
Integer,...)
+--E 43
+
+--S 44 of 134
+ode12expr:=D(yx,x) + yx**2 - 1
+--R
+--R (42)
+--R , 2 2
+--R 4y (x) + (y(x) - 1)log(y(x) + 1)
+--R
+--R +
+--R 2 2
+--R ((- 2y(x) + 2)log(y(x) - 1) - 4x y(x) + 4x)log(y(x) + 1)
+--R +
+--R 2 2 2 2 2
2
+--R (y(x) - 1)log(y(x) - 1) + (4x y(x) - 4x)log(y(x) - 1) + 4x y(x) -
4x
+--R /
+--R 2
+--R 4y(x) - 4
+--R Type: Expression
Integer
+--E 44
+
+--S 45 of 134
+ode13 := D(y(x),x) + y(x)**2 - a*x - b
+--R
+--R , 2
+--R (43) y (x) + y(x) - a x - b
+--R
+--R Type: Expression
Integer
+--E 45
+
+--S 46 of 134
+ode13a:=solve(ode13,y,x)
+--R
+--R (44) "failed"
+--R Type:
Union("failed",...)
+--E 46
+
+--S 47 of 134
+ode14 := D(y(x),x) + y(x)**2 + a*x**m
+--R
+--R
+--R , m 2
+--R (45) y (x) + a x + y(x)
+--R
+--R Type: Expression
Integer
+--E 47
+
+--S 48 of 134
+ode14a:=solve(ode14,y,x)
+--R
+--R (46) "failed"
+--R Type:
Union("failed",...)
+--E 48
+
+--S 49 of 134
+ode15 := D(y(x),x) + y(x)**2 - 2*x**2*y(x) + x**4 -2*x-1
+--R
+--R
+--R , 2 2 4
+--R (47) y (x) + y(x) - 2x y(x) + x - 2x - 1
+--R
+--R Type: Expression
Integer
+--E 49
+
+--S 50 of 134
+yx:=solve(ode15,y,x)
+--R
+--R 2
+--R y(x) - x + 1
+--R (48) ---------------------
+--R 2 2x
+--R (2y(x) - 2x - 2)%e
+--R Type: Union(Expression
Integer,...)
+--E 50
+
+--S 51 of 134
+ode15expr:=D(yx,x) + yx**2 - 2*x**2*yx + x**4 -2*x-1
+--R
+--R (49)
+--R 2x ,
+--R - 4%e y (x)
+--R
+--R +
+--R 4 2 6 4 3 2
8
+--R (4x - 8x - 4)y(x) + (- 8x - 8x + 16x + 8x + 16x + 8)y(x) +
4x
+--R +
+--R 6 5 3 2
+--R 8x - 8x - 16x - 8x - 8x - 4
+--R *
+--R 2x 2
+--R (%e )
+--R +
+--R 2 2 4 2 6 4 2 2x
+--R ((- 4x - 4)y(x) + (8x + 8x )y(x) - 4x - 4x + 4x + 8x + 4)%e
+--R +
+--R 2 2 4 2
+--R y(x) + (- 2x + 2)y(x) + x - 2x + 1
+--R /
+--R 2 2 4 2 2x 2
+--R (4y(x) + (- 8x - 8)y(x) + 4x + 8x + 4)(%e )
+--R Type: Expression
Integer
+--E 51
+
+--S 52 of 134
+ode16 := D(y(x),x) + y(x)**2 +(x*y(x)-1)*f(x)
+--R
+--R , 2
+--R (50) y (x) + y(x) + x f(x)y(x) - f(x)
+--R
+--R Type: Expression
Integer
+--E 52
+
+--S 53 of 134
+ode16a:=solve(ode16,y,x)
+--R
+--R (51) "failed"
+--R Type:
Union("failed",...)
+--E 53
+
+--S 54 of 134
+ode17 := D(y(x),x) - y(x)**2 -3*y(x) + 4
+--R
+--R
+--R , 2
+--R (52) y (x) - y(x) - 3y(x) + 4
+--R
+--R Type: Expression
Integer
+--E 54
+
+--S 55 of 134
+yx:=solve(ode17,y,x)
+--R
+--R
+--R - log(y(x) + 4) + log(y(x) - 1) - 5x
+--R (53) ------------------------------------
+--R 5
+--R Type: Union(Expression
Integer,...)
+--E 55
+
+--S 56 of 134
+ode17expr:=D(yx,x) - yx**2 -3*yx + 4
+--R
+--R (54)
+--R , 2 2
+--R 25y (x) + (- y(x) - 3y(x) + 4)log(y(x) + 4)
+--R
+--R +
+--R 2 2
+--R (2y(x) + 6y(x) - 8)log(y(x) - 1) + (- 10x + 15)y(x)
+--R +
+--R (- 30x + 45)y(x) + 40x - 60
+--R *
+--R log(y(x) + 4)
+--R +
+--R 2 2
+--R (- y(x) - 3y(x) + 4)log(y(x) - 1)
+--R +
+--R 2
+--R ((10x - 15)y(x) + (30x - 45)y(x) - 40x + 60)log(y(x) - 1)
+--R +
+--R 2 2 2 2
+--R (- 25x + 75x + 75)y(x) + (- 75x + 225x + 225)y(x) + 100x - 300x -
300
+--R /
+--R 2
+--R 25y(x) + 75y(x) - 100
+--R Type: Expression
Integer
+--E 56
+
+--S 57 of 134
+ode18 := D(y(x),x) - y(x)**2 - x*y(x) - x + 1
+--R
+--R
+--R , 2
+--R (55) y (x) - y(x) - x y(x) - x + 1
+--R
+--R Type: Expression
Integer
+--E 57
+
+--S 58 of 134
+yx:=solve(ode18,y,x)
+--R
+--R
+--R 2
+--R - x + 4x
+--R --------- x
+--R 2 ++ 1
+--I (- y(x) - 1)%e | - ------------- d%N + 1
+--R ++ 2
+--I - %N + 4%N
+--R -----------
+--R 2
+--R %e
+--R (56) ----------------------------------------------------
+--R 2
+--R - x + 4x
+--R ---------
+--R 2
+--R (y(x) + 1)%e
+--R Type: Union(Expression
Integer,...)
+--E 58
+
+--S 59 of 134
+ode18expr:=D(yx,x) - yx**2 - x*yx - x + 1
+--R (57)
+--R 2 2
+--R - x + 4x
+--R --------- x 2
+--R 2 2 ++ 1
+--I (- y(x) - 2y(x) - 1)(%e ) | - ------------- d%H
+--R ++ 2
+--I - %H + 4%H
+--R -----------
+--R 2
+--R %e
+--R +
+--R 2 2 2
+--R - x + 4x - x + 4x
+--R --------- ---------
+--R 2 2 2
+--R ((x y(x) + 2x y(x) + x)(%e ) + (2y(x) + 2)%e )
+--R *
+--R x
+--R ++ 1
+--I | - ------------- d%H
+--R ++ 2
+--I - %H + 4%H
+--R -----------
+--R 2
+--R %e
+--R +
+--R 2
+--R - x + 4x
+--R ---------
+--R 2 ,
+--R - %e y (x)
+--R
+--R +
+--R 2 2
+--R - x + 4x
+--R ---------
+--R 2 2
+--R ((- x + 1)y(x) + (- 2x + 2)y(x) - x + 1)(%e )
+--R +
+--R 2
+--R - x + 4x
+--R ---------
+--R 2 2
+--R (y(x) - 1)%e - 1
+--R /
+--R 2 2
+--R - x + 4x
+--R ---------
+--R 2 2
+--R (y(x) + 2y(x) + 1)(%e )
+--R Type: Expression
Integer
+--E 59
+
+--S 60 of 134
+ode19 := D(y(x),x) - (y(x) + x)**2
+--R
+--R
+--R , 2 2
+--R (58) y (x) - y(x) - 2x y(x) - x
+--R
+--R Type: Expression
Integer
+--E 60
+
+--S 61 of 134
+yx:=solve(ode19,y,x)
+--R
+--R
+--R +---+
+--R - y(x) + \|- 1 - x
+--R (59) --------------------------------------
+--R +---+
+--R +---+ +---+ 2x\|- 1
+--R (2\|- 1 y(x) + 2x\|- 1 - 2)%e
+--R Type: Union(Expression
Integer,...)
+--E 61
+
+--S 62 of 134
+ode19expr := D(yx,x) - (yx + x)**2
+--R
+--R (60)
+--R +---+
+--R 2x\|- 1 ,
+--R - 4%e y (x)
+--R
+--R +
+--R 2 2 2 +---+ 3 3 +---+ 4 2
+--R (- 4x y(x) + (- 8x \|- 1 - 8x )y(x) - 8x \|- 1 - 4x + 4x )
+--R *
+--R +---+ 2
+--R 2x\|- 1
+--R (%e )
+--R +
+--R +---+ 2 2 +---+ 3
+---+
+--R (- 4x\|- 1 + 4)y(x) + (- 8x \|- 1 + 8x)y(x) + (- 4x - 4x)\|-
1
+--R +
+--R 2
+--R 4x
+--R *
+--R +---+
+--R 2x\|- 1
+--R %e
+--R +
+--R 2 +---+ +---+ 2
+--R y(x) + (- 2\|- 1 + 2x)y(x) - 2x\|- 1 + x - 1
+--R /
+--R +---+ 2
+--R 2 +---+ +---+ 2 2x\|- 1
+--R (4y(x) + (8\|- 1 + 8x)y(x) + 8x\|- 1 + 4x - 4)(%e )
+--R Type: Expression
Integer
+--E 62
+
+--S 63 of 134
+ode20 := D(y(x),x) - y(x)**2 +(x**2 + 1)*y(x) - 2*x
+--R
+--R
+--R , 2 2
+--R (61) y (x) - y(x) + (x + 1)y(x) - 2x
+--R
+--R Type: Expression
Integer
+--E 63
+
+--S 64 of 134
+yx:=solve(ode20,y,x)
+--R
+--R 3
+--R - x - 3x
+--R --------- x
+--R 2 3 ++ 1
+--I (- y(x) + x + 1)%e | - ------------- d%H + 1
+--R ++ 3
+--I - %H - 3%H
+--R -----------
+--R 3
+--R %e
+--R (62) ---------------------------------------------------------
+--R 3
+--R - x - 3x
+--R ---------
+--R 2 3
+--R (y(x) - x - 1)%e
+--R Type: Union(Expression
Integer,...)
+--E 64
+
+--S 65 of 134
+ode20expr:=D(yx,x) - yx**2 +(x**2 + 1)*yx - 2*x
+--R
+--R (63)
+--R 3 2
+--R - x - 3x
+--R ---------
+--R 2 2 4 2 3
+--R (- y(x) + (2x + 2)y(x) - x - 2x - 1)(%e )
+--R *
+--R x 2
+--R ++ 1
+--I | - ------------- d%H
+--R ++ 3
+--I - %H - 3%H
+--R -----------
+--R 3
+--R %e
+--R +
+--R 2 2 4 2 6 4 2
+--R ((- x - 1)y(x) + (2x + 4x + 2)y(x) - x - 3x - 3x - 1)
+--R *
+--R 3 2
+--R - x - 3x
+--R ---------
+--R 3
+--R (%e )
+--R +
+--R 3
+--R - x - 3x
+--R ---------
+--R 2 3
+--R (2y(x) - 2x - 2)%e
+--R *
+--R x
+--R ++ 1
+--I | - ------------- d%H
+--R ++ 3
+--I - %H - 3%H
+--R -----------
+--R 3
+--R %e
+--R +
+--R 3
+--R - x - 3x
+--R ---------
+--R 3 ,
+--R - %e y (x)
+--R
+--R +
+--R 3 2
+--R - x - 3x
+--R ---------
+--R 2 3 5 3 3
+--R (- 2x y(x) + (4x + 4x)y(x) - 2x - 4x - 2x)(%e )
+--R +
+--R 3
+--R - x - 3x
+--R ---------
+--R 2 4 2 3
+--R (y(x) - x - 2x + 2x - 1)%e - 1
+--R /
+--R 3 2
+--R - x - 3x
+--R ---------
+--R 2 2 4 2 3
+--R (y(x) + (- 2x - 2)y(x) + x + 2x + 1)(%e )
+--R Type: Expression
Integer
+--E 65
+
+--S 66 of 134
+ode21 := D(y(x),x) - y(x)**2 +y(x)*sin(x) - cos(x)
+--R
+--R
+--R , 2
+--R (64) y (x) + y(x)sin(x) - cos(x) - y(x)
+--R
+--R Type: Expression
Integer
+--E 66
+
+--S 67 of 134
+ode21a:=solve(ode21,y,x)
+--R
+--R
+--R (65) "failed"
+--R Type:
Union("failed",...)
+--E 67
+
+--S 68 of 134
+ode22 := D(y(x),x) - y(x)**2 -y(x)*sin(2*x) - cos(2*x)
+--R
+--R
+--R , 2
+--R (66) y (x) - y(x)sin(2x) - cos(2x) - y(x)
+--R
+--R Type: Expression
Integer
+--E 68
+
+--S 69 of 134
+ode22a:=solve(ode22,y,x)
+--R
+--R
+--R (67) "failed"
+--R Type:
Union("failed",...)
+--E 69
+
+--S 70 of 134
+ode23 := D(y(x),x) + a*y(x)**2 - b
+--R
+--R
+--R , 2
+--R (68) y (x) + a y(x) - b
+--R
+--R Type: Expression
Integer
+--E 70
+
+--S 71 of 134
+yx:=solve(ode23,y,x)
+--R
+--R
+--R 2 +---+
+--R (a y(x) + b)\|a b - 2a b y(x) +---+
+--R log(-------------------------------) + 2x\|a b
+--R 2
+--R a y(x) - b
+--R (69) -----------------------------------------------
+--R +---+
+--R 2\|a b
+--R Type: Union(Expression
Integer,...)
+--E 71
+
+--S 72 of 134
+ode23expr := D(yx,x) + a*yx**2 - b
+--R
+--R (70)
+--R 2 +---+ 2
+--R , 2 (a y(x) + b)\|a b - 2a b y(x)
+--R 4by (x) + (a y(x) - b)log(-------------------------------)
+--R 2
+--R a y(x) - b
+--R +
+--R 2 +---+
+--R 2 +---+ (a y(x) + b)\|a b - 2a b y(x)
+--R (4a x y(x) - 4b x)\|a b log(-------------------------------)
+--R 2
+--R a y(x) - b
+--R +
+--R 2 2 2 2 2 2 3 2
+--R (4a b x - 4a b + 4a b)y(x) - 4a b x + 4b - 4b
+--R /
+--R 2 2
+--R 4a b y(x) - 4b
+--R Type: Expression
Integer
+--E 72
+
+--S 73 of 134
+ode24 := D(y(x),x) + a*y(x)**2 - b*x**nu
+--R
+--R
+--R , nu 2
+--R (71) y (x) - b x + a y(x)
+--R
+--R Type: Expression
Integer
+--E 73
+
+--S 74 of 134
+ode24a:=solve(ode24,y,x)
+--R
+--R
+--R (72) "failed"
+--R Type:
Union("failed",...)
+--E 74
+
+--S 75 of 134
+ode25 := D(y(x),x) + a*y(x)**2 - b*x**(2*nu) - c*x**(nu-1)
+--R
+--R
+--R , 2nu nu - 1 2
+--R (73) y (x) - b x - c x + a y(x)
+--R
+--R Type: Expression
Integer
+--E 75
+
+--S 76 of 134
+ode25expr:=solve(ode25,y,x)
+--R
+--R
+--R (74) "failed"
+--R Type:
Union("failed",...)
+--E 76
+
+--S 77 of 134
+ode26 := D(y(x),x) - (A*y(x) - a)*(B*y(x) - b)
+--R
+--R
+--R , 2
+--R (75) y (x) - A B y(x) + (A b + B a)y(x) - a b
+--R
+--R Type: Expression
Integer
+--E 77
+
+--S 78 of 134
+yx:=solve(ode26,y,x)
+--R
+--R
+--R log(B y(x) - b) - log(A y(x) - a) + (- A b + B a)x
+--R (76) --------------------------------------------------
+--R A b - B a
+--R Type: Union(Expression
Integer,...)
+--E 78
+
+--S 79 of 134
+ode26expr := D(yx,x) - (A*yx - a)*(B*yx - b)
+--R
+--R (77)
+--R 2 2 2 2 ,
+--R (A b - 2A B a b + B a )y (x)
+--R
+--R +
+--R 2 2 2 2 2 2
+--R (- A B y(x) + (A B b + A B a)y(x) - A B a b)log(B y(x) - b)
+--R +
+--R 2 2 2 2 2
+--R (2A B y(x) + (- 2A B b - 2A B a)y(x) + 2A B a b)log(A y(x) - a)
+--R +
+--R 3 2 2 3 3 2 3 2 2
+--R ((2A B b - 2A B a)x + A B b - A B a )y(x)
+--R +
+--R 3 2 3 2 3 3 2 2 2 2 3 3
+--R ((- 2A B b + 2A B a )x - A b - A B a b + A B a b + B a )y(x)
+--R +
+--R 2 2 2 2 2 3 2 3
+--R (2A B a b - 2A B a b)x + A a b - B a b
+--R *
+--R log(B y(x) - b)
+--R +
+--R 2 2 2 2 2 2
+--R (- A B y(x) + (A B b + A B a)y(x) - A B a b)log(A y(x) - a)
+--R +
+--R 3 2 2 3 3 2 3 2 2
+--R ((- 2A B b + 2A B a)x - A B b + A B a )y(x)
+--R +
+--R 3 2 3 2 3 3 2 2 2 2 3 3
+--R ((2A B b - 2A B a )x + A b + A B a b - A B a b - B a )y(x)
+--R +
+--R 2 2 2 2 2 3 2 3
+--R (- 2A B a b + 2A B a b)x - A a b + B a b
+--R *
+--R log(A y(x) - a)
+--R +
+--R 4 2 2 3 3 2 4 2 2
+--R (- A B b + 2A B a b - A B a )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 3 3
+--R (- A B b + A B a b + A B a b - A B a )x - A B a b
+--R +
+--R 2 2 2 3 2 3 3 2 2 3 2
+--R (2A B a - A B)b + (- A B a + 2A B a)b - A B a
+--R *
+--R 2
+--R y(x)
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 2 4 4 2 2 2 2
4 4
+--R (A B b - A B a b - A B a b + A B a )x + (A b - 2A B a b + B
a )x
+--R +
+--R 3 4 2 2 3 3 2 3 2 2 3 4 2
2
+--R A a b + (- A B a + A )b + (- A B a - A B a)b + (B a - A B
a )b
+--R +
+--R 3 3
+--R B a
+--R *
+--R y(x)
+--R +
+--R 3 3 2 2 2 2 3 3 2
+--R (- A B a b + 2A B a b - A B a b)x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 2 4 3 2
3
+--R (- A a b + A B a b + A B a b - B a b)x - A a b + (2A B a - A a)b
+--R +
+--R 2 4 2 2 2 3
+--R (- B a + 2A B a )b - B a b
+--R /
+--R 3 2 2 2 3 2 2
+--R (A B b - 2A B a b + A B a )y(x)
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2 3
+--R (- A b + A B a b + A B a b - B a )y(x) + A a b - 2A B a b + B a b
+--R Type: Expression
Integer
+--E 79
+
+--S 80 of 134
+ode27 := D(y(x),x) + a*y(x)*(y(x)-x) - 1
+--R
+--R
+--R , 2
+--R (78) y (x) + a y(x) - a x y(x) - 1
+--R
+--R Type: Expression
Integer
+--E 80
+
+--S 81 of 134
+ode27a:=solve(ode27,y,x)
+--R
+--R
+--R 2
+--R a x
+--R ---- x
+--R 2 ++ a
+--I (- y(x) + x)%e | ------ d%N + 1
+--R ++ 2
+--I %N a
+--R ----
+--R 2
+--R %e
+--R (79) --------------------------------------
+--R 2
+--R a x
+--R ----
+--R 2
+--R (y(x) - x)%e
+--R Type: Union(Expression
Integer,...)
+--E 81
+
+--S 82 of 134
+ode28 := D(y(x),x) + x*y(x)**2 -x**3*y(x) - 2*x
+--R
+--R
+--R , 2 3
+--R (80) y (x) + x y(x) - x y(x) - 2x
+--R
+--R Type: Expression
Integer
+--E 82
+
+--S 83 of 134
+ode28a:=solve(ode28,y,x)
+--R
+--R
+--R 4
+--R x
+--R -- x
+--I 2 4 ++ %N
+--I (- y(x) + x )%e | ----- d%N + 1
+--R ++ 4
+--I %N
+--R ---
+--R 4
+--R %e
+--R (81) ------------------------------------
+--R 4
+--R x
+--R --
+--R 2 4
+--R (y(x) - x )%e
+--R Type: Union(Expression
Integer,...)
+--E 83
+
+--S 84 of 134
+ode29 := D(y(x),x) - x*y(x)**2 - 3*x*y(x)
+--R
+--R
+--R , 2
+--R (82) y (x) - x y(x) - 3x y(x)
+--R
+--R Type: Expression
Integer
+--E 84
+
+--S 85 of 134
+yx:=solve(ode29,y,x)
+--R
+--R
+--R 2
+--R - 2log(y(x) + 3) + 2log(y(x)) - 3x
+--R (83) -----------------------------------
+--R 6
+--R Type: Union(Expression
Integer,...)
+--E 85
+
+--S 86 of 134
+ode29expr := D(yx,x) - x*yx**2 - 3*x*yx
+--R
+--R (84)
+--R , 2 2
+--R 36y (x) + (- 4x y(x) - 12x y(x))log(y(x) + 3)
+--R
+--R +
+--R 2 3 2
+--R (8x y(x) + 24x y(x))log(y(x)) + (- 12x + 36x)y(x)
+--R +
+--R 3
+--R (- 36x + 108x)y(x)
+--R *
+--R log(y(x) + 3)
+--R +
+--R 2 2
+--R (- 4x y(x) - 12x y(x))log(y(x))
+--R +
+--R 3 2 3
+--R ((12x - 36x)y(x) + (36x - 108x)y(x))log(y(x))
+--R +
+--R 5 3 2 5 3
+--R (- 9x + 54x - 36x)y(x) + (- 27x + 162x - 108x)y(x)
+--R /
+--R 2
+--R 36y(x) + 108y(x)
+--R Type: Expression
Integer
+--E 86
+
+--S 87 of 134
+ode30 := D(y(x),x) + x**(-a-1)*y(x)**2 - x**a
+--R
+--R
+--R , a 2 - a - 1
+--R (85) y (x) - x + y(x) x
+--R
+--R Type: Expression
Integer
+--E 87
+
+--S 88 of 134
+ode30a:=solve(ode30,y,x)
+--R
+--R
+--R (86) "failed"
+--R Type:
Union("failed",...)
+--E 88
+
+--S 89 of 134
+ode31 := D(y(x),x) - a*x**n*(y(x)**2+1)
+--R
+--R
+--R , 2 n
+--R (87) y (x) + (- a y(x) - a)x
+--R
+--R Type: Expression
Integer
+--E 89
+
+--S 90 of 134
+yx:=solve(ode31,y,x)
+--R
+--R
+--R n log(x)
+--R - a x %e + (n + 1)atan(y(x))
+--R (88) ------------------------------------
+--R n + 1
+--R Type: Union(Expression
Integer,...)
+--E 90
+
+--S 91 of 134
+ode31expr := D(yx,x) - a*x**n*(yx**2+1)
+--R
+--R (89)
+--R 2 , 3 2 2 3 2 n n log(x) 2
+--R (n + 2n + 1)y (x) + (- a x y(x) - a x )x (%e )
+--R
+--R +
+--R 2 2 2 2 2 n
+--R ((2a n + 2a )x y(x) + (2a n + 2a )x)x atan(y(x))
+--R +
+--R 2 2 2
+--R (- a n - 2a n - a)y(x) - a n - 2a n - a
+--R *
+--R n log(x)
+--R %e
+--R +
+--R 2 2 2 n 2
+--R ((- a n - 2a n - a)y(x) - a n - 2a n - a)x atan(y(x))
+--R +
+--R 2 2 2 n
+--R ((- a n - 2a n - a)y(x) - a n - 2a n - a)x
+--R /
+--R 2 2 2
+--R (n + 2n + 1)y(x) + n + 2n + 1
+--R Type: Expression
Integer
+--E 91
+
+--S 92 of 134
+ode32 := D(y(x),x) + y(x)**2*sin(x) - 2*sin(x)/cos(x)**2
+--R
+--R
+--R 2 , 2 2
+--R cos(x) y (x) + (y(x) cos(x) - 2)sin(x)
+--R
+--R (90) ---------------------------------------
+--R 2
+--R cos(x)
+--R Type: Expression
Integer
+--E 92
+
+--S 93 of 134
+yx:=solve(ode32,y,x)
+--R
+--R
+--R (91) "failed"
+--R Type:
Union("failed",...)
+--E 93
+
+--S 94 of 134
+ode33 := D(y(x),x) - y(x)**2*D(f(x),x)/g(x) + D(g(x),x)/f(x)
+--R
+--R , , 2 ,
+--R f(x)g(x)y (x) + g(x)g (x) - f(x)y(x) f (x)
+--R
+--R (92) ------------------------------------------
+--R f(x)g(x)
+--R Type: Expression
Integer
+--E 94
+
+--S 95 of 134
+ode33a:=solve(ode33,y,x)
+--R
+--R (93) "failed"
+--R Type:
Union("failed",...)
+--E 95
+
+--S 96 of 134
+ode34 := D(y(x),x) + f(x)*y(x)**2 + g(x)*y(x)
+--R
+--R , 2
+--R (94) y (x) + f(x)y(x) + g(x)y(x)
+--R
+--R Type: Expression
Integer
+--E 96
+
+--S 97 of 134
+ode34a:=solve(ode34,y,x)
+--R
+--R
+--R >> Error detected within library code:
+--R Function not supported by Risch d.e.
+--R
+--R Continuing to read the file...
+--R
+--E 97
+
+--S 98 of 134
+ode35 := D(y(x),x) + f(x)*(y(x)**2 + 2*a*y(x) +b)
+--R
+--R , 2
+--R (95) y (x) + f(x)y(x) + 2a f(x)y(x) + b f(x)
+--R
+--R Type: Expression
Integer
+--E 98
+
+--S 99 of 134
+yx:=solve(ode35,y,x)
+--R
+--R (96)
+--R +--------+ x
+--R | 2 ++
+--I 2\|- b + a | f(%H)d%H
+--R ++
+--R +
+--R +--------+
+--R 2 2 | 2 2
3
+--R (y(x) + 2a y(x) - b + 2a )\|- b + a + (2b - 2a )y(x) + 2a b - 2a
+--R
log(--------------------------------------------------------------------)
+--R 2
+--R y(x) + 2a y(x) + b
+--R /
+--R +--------+
+--R | 2
+--R 2\|- b + a
+--R Type: Union(Expression
Integer,...)
+--E 99
+
+--S 100 of 134
+ode35expr := D(yx,x) + f(x)*(yx**2 + 2*a*yx +b)
+--R
+--R (97)
+--R 2 2 3 2 2
+--R ((4b - 4a )f(x)y(x) + (8a b - 8a )f(x)y(x) + (4b - 4a b)f(x))
+--R *
+--R +--------+ x 2
+--R | 2 ++
+--I \|- b + a | f(%H)d%H
+--R ++
+--R +
+--R 2 2 3 2 2
+--R ((4b - 4a )f(x)y(x) + (8a b - 8a )f(x)y(x) + (4b - 4a b)f(x))
+--R *
+--R log
+--R +--------+
+--R 2 2 | 2 2
+--R (y(x) + 2a y(x) - b + 2a )\|- b + a + (2b - 2a )y(x)
+--R +
+--R 3
+--R 2a b - 2a
+--R /
+--R 2
+--R y(x) + 2a y(x) + b
+--R +
+--R 3 2 2 4
+--R (8a b - 8a )f(x)y(x) + (16a b - 16a )f(x)y(x)
+--R +
+--R 2 3
+--R (8a b - 8a b)f(x)
+--R *
+--R +--------+
+--R | 2
+--R \|- b + a
+--R *
+--R x
+--R ++
+--I | f(%H)d%H
+--R ++
+--R +
+--R +--------+
+--R 2 | 2 ,
+--R (4b - 4a )\|- b + a y (x)
+--R
+--R +
+--R +--------+
+--R 2 | 2
+--R (- f(x)y(x) - 2a f(x)y(x) - b f(x))\|- b + a
+--R *
+--R log
+--R +--------+
+--R 2 2 | 2 2
+--R (y(x) + 2a y(x) - b + 2a )\|- b + a + (2b - 2a )y(x) +
2a b
+--R +
+--R 3
+--R - 2a
+--R /
+--R 2
+--R y(x) + 2a y(x) + b
+--R **
+--R 2
+--R +
+--R 3 2 2 4 2 3
+--R ((4a b - 4a )f(x)y(x) + (8a b - 8a )f(x)y(x) + (4a b - 4a b)f(x))
+--R *
+--R +--------+
+--R 2 2 | 2 2
3
+--R (y(x) + 2a y(x) - b + 2a )\|- b + a + (2b - 2a )y(x) + 2a b -
2a
+--R
log(--------------------------------------------------------------------)
+--R 2
+--R y(x) + 2a y(x) + b
+--R +
+--R 2 2 2 2
+--R (4b + (- 4a + 4)b - 4a )f(x)y(x)
+--R +
+--R 2 3 3
+--R (8a b + (- 8a + 8a)b - 8a )f(x)y(x)
+--R +
+--R 3 2 2 2
+--R (4b + (- 4a + 4)b - 4a b)f(x)
+--R *
+--R +--------+
+--R | 2
+--R \|- b + a
+--R /
+--R +--------+
+--R 2 2 3 2 2 | 2
+--R ((4b - 4a )y(x) + (8a b - 8a )y(x) + 4b - 4a b)\|- b + a
+--R Type: Expression
Integer
+--E 100
+
+--S 101 of 134
+ode36 := D(y(x),x) + y(x)**3 + a*x*y(x)**2
+--R
+--R
+--R , 3 2
+--R (98) y (x) + y(x) + a x y(x)
+--R
+--R Type: Expression
Integer
+--E 101
+
+--S 102 of 134
+ode36a:=solve(ode36,y,x)
+--R
+--R
+--R (99) "failed"
+--R Type:
Union("failed",...)
+--E 102
+
+--S 103 of 134
+ode37 := D(y(x),x) - y(x)**3 - a*exp(x)*y(x)**2
+--R
+--R , 2 x 3
+--R (100) y (x) - a y(x) %e - y(x)
+--R
+--R Type: Expression
Integer
+--E 103
+
+--S 104 of 134
+ode37a:=solve(ode37,y,x)
+--R
+--R (101) "failed"
+--R Type:
Union("failed",...)
+--E 104
+
+--S 105 of 134
+ode38 := D(y(x),x) - a*y(x)**3 - b*x**(3/2)
+--R
+--R , +-+ 3
+--R (102) y (x) - b x\|x - a y(x)
+--R
+--R Type: Expression
Integer
+--E 105
+
+--S 106 of 134
+ode38a:=solve(ode38,y,x)
+--R
+--R (103) "failed"
+--R Type:
Union("failed",...)
+--E 106
+
+--S 107 of 134
+ode39 := D(y(x),x) - a3*y(x)**3 - a2*y(x)**2 - a1*y(x) - a0
+--R
+--R , 3 2
+--R (104) y (x) - a3 y(x) - a2 y(x) - a1 y(x) - a0
+--R
+--R Type: Expression
Integer
+--E 107
+
+--S 108 of 134
+yx:=solve(ode39,y,x)
+--R
+--R
+--R (105)
+--R ROOT
+--R 2 2 3 3 2
2
+--R (- 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2 + 3a1
a2 )
+--R *
+--R 2
+--I %%CK0
+--R +
+--R 2
+--R 12a1 a3 - 4a2
+--R /
+--R 2 2 3 3 2 2
+--R 27a0 a3 + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2 - a1 a2
+--R +
+--I - %%CK0
+--R *
+--R log
+--R 2 3 2 2 2 4 2
+--R 162a0 a1 a3 + (- 54a0 a2 - 108a0 a1 a2 + 24a1 )a3
+--R +
+--R 3 3 2 5 2 4
+--R (60a0 a1 a2 - 14a1 a2 )a3 - 8a0 a2 + 2a1 a2
+--R *
+--I %%CK0
+--R +
+--R 2 3 3 2 3 2 2
+--R 81a0 a3 + (- 54a0 a1 a2 + 12a1 )a3 + (12a0 a2 - 3a1 a2
)a3
+--R *
+--R ROOT
+--R 2 2 3 3
+--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2
+--R +
+--R 2 2
+--R 3a1 a2
+--R *
+--R 2
+--I %%CK0
+--R +
+--R 2
+--R 12a1 a3 - 4a2
+--R /
+--R 2 2 3 3 2 2
+--R 27a0 a3 + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2 - a1 a2
+--R +
+--R 2 3 2 2 2 4 2
+--R 162a0 a1 a3 + (- 54a0 a2 - 108a0 a1 a2 + 24a1 )a3
+--R +
+--R 3 3 2 5 2 4
+--R (60a0 a1 a2 - 14a1 a2 )a3 - 8a0 a2 + 2a1 a2
+--R *
+--R 2
+--I %%CK0
+--R +
+--R 2 3 3 2
+--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3
+--R +
+--R 3 2 2
+--R (- 12a0 a2 + 3a1 a2 )a3
+--R *
+--I %%CK0
+--R +
+--R 3 2 3 2 2
+--R (54a0 a3 - 18a1 a2 a3 + 4a2 a3)y(x) + (18a0 a2 - 12a1 )a3
+--R +
+--R 2
+--R 2a1 a2 a3
+--R +
+--R -
+--R ROOT
+--R 2 2 3 3
+--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2
+--R +
+--R 2 2
+--R 3a1 a2
+--R *
+--R 2
+--I %%CK0
+--R +
+--R 2
+--R 12a1 a3 - 4a2
+--R /
+--R 2 2 3 3 2 2
+--R 27a0 a3 + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2 - a1 a2
+--R +
+--I - %%CK0
+--R *
+--R log
+--R 2 3 2 2 2 4 2
+--R - 162a0 a1 a3 + (54a0 a2 + 108a0 a1 a2 - 24a1 )a3
+--R +
+--R 3 3 2 5 2 4
+--R (- 60a0 a1 a2 + 14a1 a2 )a3 + 8a0 a2 - 2a1 a2
+--R *
+--I %%CK0
+--R +
+--R 2 3 3 2 3 2 2
+--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 + (- 12a0 a2 + 3a1 a2
)a3
+--R *
+--R ROOT
+--R 2 2 3 3
+--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2
+--R +
+--R 2 2
+--R 3a1 a2
+--R *
+--R 2
+--I %%CK0
+--R +
+--R 2
+--R 12a1 a3 - 4a2
+--R /
+--R 2 2 3 3 2 2
+--R 27a0 a3 + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2 - a1 a2
+--R +
+--R 2 3 2 2 2 4 2
+--R 162a0 a1 a3 + (- 54a0 a2 - 108a0 a1 a2 + 24a1 )a3
+--R +
+--R 3 3 2 5 2 4
+--R (60a0 a1 a2 - 14a1 a2 )a3 - 8a0 a2 + 2a1 a2
+--R *
+--R 2
+--I %%CK0
+--R +
+--R 2 3 3 2
+--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3
+--R +
+--R 3 2 2
+--R (- 12a0 a2 + 3a1 a2 )a3
+--R *
+--I %%CK0
+--R +
+--R 3 2 3 2 2
+--R (54a0 a3 - 18a1 a2 a3 + 4a2 a3)y(x) + (18a0 a2 - 12a1 )a3
+--R +
+--R 2
+--R 2a1 a2 a3
+--R +
+--I 2%%CK0
+--R *
+--R log
+--R 2 3 2 2 2 4 2
+--R - 162a0 a1 a3 + (54a0 a2 + 108a0 a1 a2 - 24a1 )a3
+--R +
+--R 3 3 2 5 2 4
+--R (- 60a0 a1 a2 + 14a1 a2 )a3 + 8a0 a2 - 2a1 a2
+--R *
+--R 2
+--I %%CK0
+--R +
+--R 2 3 3 2 3 2 2
+--R (81a0 a3 + (- 54a0 a1 a2 + 12a1 )a3 + (12a0 a2 - 3a1 a2
)a3)
+--R *
+--I %%CK0
+--R +
+--R 3 2 3 2 2
+--R (27a0 a3 - 9a1 a2 a3 + 2a2 a3)y(x) + (9a0 a2 + 12a1 )a3
+--R +
+--R 2 4
+--R - 11a1 a2 a3 + 2a2
+--R +
+--R - 2x
+--R /
+--R 2
+--R Type: Union(Expression
Integer,...)
+--E 108
+
+--S 109 of 134
+ode40 := D(y(x),x) + 3*a*y(x)**3 + 6*a*x*y(x)**2
+--R
+--R , 3 2
+--R (106) y (x) + 3a y(x) + 6a x y(x)
+--R
+--R Type: Expression
Integer
+--E 109
+
+--S 110 of 134
+ode40a:=solve(ode40,y,x)
+--R
+--R (107) "failed"
+--R Type:
Union("failed",...)
+--E 110
+
+--S 111 of 134
+ode41 := D(y(x),x) + a*x*y(x)**3 + b*y(x)**2
+--R
+--R , 3 2
+--R (108) y (x) + a x y(x) + b y(x)
+--R
+--R Type: Expression
Integer
+--E 111
+
+--S 112 of 134
+ode41a:=solve(ode41,y,x)
+--R
+--R (109) "failed"
+--R Type:
Union("failed",...)
+--E 112
+
+--S 113 of 134
+ode42 := D(y(x),x) - x*(x+2)*y(x)**3 - (x+3)*y(x)**2
+--R
+--R , 2 3 2
+--R (110) y (x) + (- x - 2x)y(x) + (- x - 3)y(x)
+--R
+--R Type: Expression
Integer
+--E 113
+
+--S 114 of 134
+ode42a:=solve(ode42,y,x)
+--R
+--R (111) "failed"
+--R Type:
Union("failed",...)
+--E 114
+
+--S 115 of 134
+ode43 := D(y(x),x) + (3*a*x**2 + 4*a**2*x + b)*y(x)**3 + 3*x*y(x)**2
+--R
+--R , 2 2 3 2
+--R (112) y (x) + (3a x + 4a x + b)y(x) + 3x y(x)
+--R
+--R Type: Expression
Integer
+--E 115
+
+--S 116 of 134
+ode43a:=solve(ode43,y,x)
+--R
+--R (113) "failed"
+--R Type:
Union("failed",...)
+--E 116
+
+--S 117 of 134
+ode44 := D(y(x),x) + 2*a*x**3*y(x)**3 + 2*x*y(x)
+--R
+--R , 3 3
+--R (114) y (x) + 2a x y(x) + 2x y(x)
+--R
+--R Type: Expression
Integer
+--E 117
+
+--S 118 of 134
+yx:=solve(ode44,y,x)
+--R
+--R 2 2
+--R (2a x + a)y(x) + 2
+--R (115) --------------------
+--R 2
+--R 2 2x
+--R 2y(x) %e
+--R Type: Union(Expression
Integer,...)
+--E 118
+
+--S 119 of 134
+ode44expr := D(yx,x) + 2*a*x**3*yx**3 + 2*x*yx
+--R
+--R (116)
+--R 2 2 2 2
+--R 3 2x , 3 6 4 2x
+--R - 8y(x) (%e ) y (x) + ((- 8a x + 4a x)y(x) - 8x y(x) )(%e )
+--R
+--R +
+--R 4 9 4 7 4 5 4 3 6 3 7 3 5 3 3 4
+--R (8a x + 12a x + 6a x + a x )y(x) + (24a x + 24a x + 6a x )y(x)
+--R +
+--R 2 5 2 3 2 3
+--R (24a x + 12a x )y(x) + 8a x
+--R /
+--R 2 3
+--R 6 2x
+--R 4y(x) (%e )
+--R Type: Expression
Integer
+--E 119
+
+--S 120 of 134
+ode45 := D(y(x),x) + 2*(a**2*x**3 - b**2*x)*y(x)**3 + 3*b*y(x)**2
+--R
+--R , 2 3 2 3 2
+--R (117) y (x) + (2a x - 2b x)y(x) + 3b y(x)
+--R
+--R Type: Expression
Integer
+--E 120
+
+--S 121 of 134
+ode45a:=solve(ode45,y,x)
+--R
+--R (118) "failed"
+--R Type:
Union("failed",...)
+--E 121
+
+--S 122 of 134
+ode46 := D(y(x),x) - x**a*y(x)**3 + 3*y(x)**2 - x**(-a)*y(x) _
+ -x**(-2*a) + a*x**(-a-1)
+--R
+--R , 3 a - a - a - 1 - 2a 2
+--R (119) y (x) - y(x) x - y(x)x + a x - x + 3y(x)
+--R
+--R Type: Expression
Integer
+--E 122
+
+--S 123 of 134
+ode46a:=solve(ode46,y,x)
+--R
+--R (120) "failed"
+--R Type:
Union("failed",...)
+--E 123
+
+--S 124 of 134
+ode47 := D(y(x),x) - a*(x**n - x)*y(x)**3 - y(x)**2
+--R
+--R , 3 n 3 2
+--R (121) y (x) - a y(x) x + a x y(x) - y(x)
+--R
+--R Type: Expression
Integer
+--E 124
+
+--S 125 of 134
+ode47a:=solve(ode47,y,x)
+--R
+--R (122) "failed"
+--R Type:
Union("failed",...)
+--E 125
+
+--S 126 of 134
+ode48 := D(y(x),x) - (a*x**n + b*x)*y(x)**3 - c*y(x)**2
+--R
+--R , 3 n 3 2
+--R (123) y (x) - a y(x) x - b x y(x) - c y(x)
+--R
+--R Type: Expression
Integer
+--E 126
+
+--S 127 of 134
+ode48a:=solve(ode48,y,x)
+--R
+--R (124) "failed"
+--R Type:
Union("failed",...)
+--E 127
+
+--S 128 of 134
+ode49 := D(y(x),x) + a*diff(phi(x),x)*y(x)**3 + 6*a*phi(x)*y(x)**2 + _
+ (2*a+1)*y(x)*diff(phi(x),x,x)/diff(phi(x),x) +2*(a+1)
+--R
+--R There are no library operations named phi
+--R Use HyperDoc Browse or issue
+--R )what op phi
+--R to learn if there is any operation containing " phi " in its
+--R name.
+--R
+--R Cannot find a definition or applicable library operation named phi
+--R with argument type(s)
+--R Variable x
+--R
+--R Perhaps you should use "@" to indicate the required return type,
+--R or "$" to specify which version of the function you need.
+--E 128
+
+--S 129 of 134
+f1 := operator 'f1
+--R
+--R (125) f1
+--R Type:
BasicOperator
+--E 129
+
+--S 130 of 134
+f2 := operator 'f2
+--R
+--R (126) f2
+--R Type:
BasicOperator
+--E 130
+
+--S 131 of 134
+f3 := operator 'f3
+--R
+--R (127) f3
+--R Type:
BasicOperator
+--E 131
+
+--S 132 of 134
+f0 := operator 'f0
+--R
+--R (128) f0
+--R Type:
BasicOperator
+--E 132
+
+--S 133 of 134
+ode50 := D(y(x),x) - f3(x)*y(x)**3 - f2(x)*y(x)**2 - f1(x)*y(x) - f0(x)
+--R
+--R , 3 2
+--R (129) y (x) - f3(x)y(x) - f2(x)y(x) - f1(x)y(x) - f0(x)
+--R
+--R Type: Expression
Integer
+--E 133
+
+--S 134 of 134
+ode50a:=solve(ode50,y,x)
+--R
+--R (130) "failed"
+--R Type:
Union("failed",...)
+--E 134
+
+)spool
+)lisp (bye)
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} {\bf http://www.cs.uwaterloo.ca/$\tilde{}$ecterrab/odetools.html}
+\end{thebibliography}
+\end{document}
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