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}