diff --git a/changelog b/changelog index 2e818cc..666bd42 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,5 @@ +20071005 tpd src/input/Makefile kamke4.input regression test added +20071005 tpd src/input/kamke4.input ODE regression test added 20071005 tpd src/input/Makefile kamke3.input regression test added 20071005 tpd src/input/kamke3.input ODE regression test added 20071004 tpd src/input/Makefile kamke2.input regression test added diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 1bda3be..b803938 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -323,6 +323,7 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress alist.regress \ iprntpk.regress \ ipftest.regress is.regress isprime.regress kafile.regress \ kamke0.regress kamke1.regress kamke2.regress kamke3.regress \ + kamke4.regress \ kernel.regress knot2.regress kovacic.regress kuipers.regress \ laplace.regress leg.regress limit.regress lindep.regress \ list.regress lode.regress lodesys.regress lodo1.regress \ @@ -562,7 +563,7 @@ 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}/kamke3.input \ + ${OUT}/kamke2.input ${OUT}/kamke3.input ${OUT}/kamke4.input \ ${OUT}/kernel.input ${OUT}/knot.input \ ${OUT}/kovacic.input ${OUT}/kuipers.input \ ${OUT}/laplace.input ${OUT}/leg.input ${OUT}/lexp.input \ @@ -830,6 +831,7 @@ DOCFILES= \ ${DOC}/isprime.input.dvi ${DOC}/kafile.input.dvi \ ${DOC}/kamke0.input.dvi ${DOC}/kamke1.input.dvi \ ${DOC}/kamke2.input.dvi ${DOC}/kamke3.input.dvi \ + ${DOC}/kamke4.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/kamke4.input.pamphlet b/src/input/kamke4.input.pamphlet new file mode 100644 index 0000000..57e395d --- /dev/null +++ b/src/input/kamke4.input.pamphlet @@ -0,0 +1,1462 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input kamke4.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This is the 201-250 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 kamke4.output +)set break resume +)set mes auto off +)clear all +--S 1 of 127 +y:=operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 1 + +--S 2 of 127 +f:=operator 'f +--R +--R +--R (2) f +--R Type: BasicOperator +--E 2 + +--S 3 of 127 +f0:=operator 'f0 +--R +--R +--R (3) f0 +--R Type: BasicOperator +--E 3 + +--S 4 of 127 +f1:=operator 'f1 +--R +--R +--R (4) f1 +--R Type: BasicOperator +--E 4 + +--S 5 of 127 +f2:=operator 'f2 +--R +--R +--R (5) f2 +--R Type: BasicOperator +--E 5 + +--S 6 of 127 +g:=operator 'g +--R +--R +--R (6) g +--R Type: BasicOperator +--E 6 + +--S 7 of 127 +tg:=operator 'tg +--R +--R +--R (7) tg +--R Type: BasicOperator +--E 7 + +--S 8 of 127 +h:=operator 'h +--R +--R +--R (8) h +--R Type: BasicOperator +--E 8 + +--S 9 of 127 +ode201 := 2*f(x)*D(y(x),x)+2*f(x)*y(x)**2-D(f(x),x)*y(x)-2*f(x)**2 +--R +--R +--R , , 2 2 +--R (9) 2f(x)y (x) - y(x)f (x) + 2f(x)y(x) - 2f(x) +--R +--R Type: Expression Integer +--E 9 + +--S 10 of 127 +solve(ode201,y,x) +--R +--R +--R (10) "failed" +--R Type: Union("failed",...) +--E 10 + +--S 11 of 127 +ode202 := f(x)*D(y(x),x)+g(x)*tg(y(x))+h(x) +--R +--R +--R , +--R (11) f(x)y (x) + g(x)tg(y(x)) + h(x) +--R +--R Type: Expression Integer +--E 11 + +--S 12 of 127 +solve(ode202,y,x) +--R +--R +--R (12) "failed" +--R Type: Union("failed",...) +--E 12 + +--S 13 of 127 +ode203 := y(x)*D(y(x),x)+y(x)+x**3 +--R +--R +--R , 3 +--R (13) y(x)y (x) + y(x) + x +--R +--R Type: Expression Integer +--E 13 + +--S 14 of 127 +solve(ode203,y,x) +--R +--R +--R (14) "failed" +--R Type: Union("failed",...) +--E 14 + +--S 15 of 127 +ode204 := y(x)*D(y(x),x)+a*y(x)+x +--R +--R +--R , +--R (15) y(x)y (x) + a y(x) + x +--R +--R Type: Expression Integer +--E 15 + +--S 16 of 127 +solve(ode204,y,x) +--R +--R +--R (16) "failed" +--R Type: Union("failed",...) +--E 16 + +--S 17 of 127 +ode205 := y(x)*D(y(x),x)+a*y(x)+(a**2-1)/(4)*x+b*x**n +--R +--R +--R , n 2 +--R 4y(x)y (x) + 4b x + 4a y(x) + (a - 1)x +--R +--R (17) ---------------------------------------- +--R 4 +--R Type: Expression Integer +--E 17 + +--S 18 of 127 +solve(ode205,y,x) +--R +--R +--R (18) "failed" +--R Type: Union("failed",...) +--E 18 + +--S 19 of 127 +ode206 := y(x)*D(y(x),x)+a*y(x)+b*exp(x)-2*a +--R +--R +--R , x +--R (19) y(x)y (x) + b %e + a y(x) - 2a +--R +--R Type: Expression Integer +--E 19 + +--S 20 of 127 +solve(ode206,y,x) +--R +--R +--R (20) "failed" +--R Type: Union("failed",...) +--E 20 + +--S 21 of 127 +ode207 := y(x)*D(y(x),x)+y(x)**2+4*x*(x+1) +--R +--R +--R , 2 2 +--R (21) y(x)y (x) + y(x) + 4x + 4x +--R +--R Type: Expression Integer +--E 21 + +--S 22 of 127 +yx:=solve(ode207,y,x) +--R +--R +--R 2 2 2x +--R (y(x) + 4x )%e +--R (22) ----------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 22 + +--S 23 of 127 +ode207expr := yx*D(yx,x)+yx**2+4*x*(x+1) +--R +--R +--R (23) +--R 3 2 2x 2 , +--R (2y(x) + 8x y(x))(%e ) y (x) +--R +--R + +--R 4 2 2 4 3 2x 2 2 +--R (3y(x) + (24x + 8x)y(x) + 48x + 32x )(%e ) + 16x + 16x +--R / +--R 4 +--R Type: Expression Integer +--E 23 + +--S 24 of 127 +ode208 := y(x)*D(y(x),x)+a*y(x)**2-b*cos(x+c) +--R +--R +--R , 2 +--R (24) y(x)y (x) - b cos(x + c) + a y(x) +--R +--R Type: Expression Integer +--E 24 + +--S 25 of 127 +yx:=solve(ode208,y,x) +--R +--R +--R 2a x 2 2 2a x +--R - 2b %e sin(x + c) + (- 4a b cos(x + c) + (4a + 1)y(x) )%e +--R (25) ------------------------------------------------------------------ +--R 2 +--R 8a + 2 +--R Type: Union(Expression Integer,...) +--E 25 + +--S 26 of 127 +ode208expr := yx*D(yx,x)+a*yx**2-b*cos(x+c) +--R +--R +--R (26) +--R 2 2a x 2 +--R (- 16a - 4)b y(x)(%e ) sin(x + c) +--R + +--R 3 4 2 3 2a x 2 +--R ((- 32a - 8a)b y(x)cos(x + c) + (32a + 16a + 2)y(x) )(%e ) +--R * +--R , +--R y (x) +--R +--R + +--R 2 2a x 2 2 +--R 4a b (%e ) sin(x + c) +--R + +--R 2 2 3 2 2a x 2 +--R ((32a + 4)b cos(x + c) + (- 32a - 8a)b y(x) )(%e ) sin(x + c) +--R + +--R 3 2 2 4 2 2 +--R (48a + 8a)b cos(x + c) + (- 96a - 32a - 2)b y(x) cos(x + c) +--R + +--R 5 3 4 +--R (48a + 24a + 3a)y(x) +--R * +--R 2a x 2 +--R (%e ) +--R + +--R 4 2 +--R (- 64a - 32a - 4)b cos(x + c) +--R / +--R 4 2 +--R 64a + 32a + 4 +--R Type: Expression Integer +--E 26 + +--S 27 of 127 +ode209 := y(x)*D(y(x),x)-sqrt(a*y(x)**2+b) +--R +--R +--R +-----------+ +--R , | 2 +--R (27) y(x)y (x) - \|a y(x) + b +--R +--R Type: Expression Integer +--E 27 + +--S 28 of 127 +yx:=solve(ode209,y,x) +--R +--R +--R +-----------+ +--R +-+ | 2 2 +-+ +--R - x\|b \|a y(x) + b + y(x) \|b + b x +--R (28) --------------------------------------- +--R +-----------+ +--R +-+ | 2 +--R \|b \|a y(x) + b - b +--R Type: Union(Expression Integer,...) +--E 28 + +--S 29 of 127 +ode209expr := yx*D(yx,x)-sqrt(a*yx**2+b) +--R +--R +--R (29) +--R +-----------+ +--R 2 2 | 2 2 4 2 2 +-+ +--R ((- 3a b y(x) - 4b )\|a y(x) + b + (a y(x) + 5a b y(x) + 4b )\|b ) +--R * +--R ROOT +--R +-----------+ +--R 2 +-+ 2 | 2 2 +-+ +--R ((2a x + 2b)\|b + 2a x y(x) )\|a y(x) + b - 2a x y(x) \|b +--R + +--R 4 2 2 2 2 2 +--R - a y(x) + (- a x - a b)y(x) - 2a b x - 2b +--R / +--R +-----------+ +--R +-+ | 2 2 +--R 2\|b \|a y(x) + b - a y(x) - 2b +--R + +--R +-----------+ +--R 3 +-+ 3 | 2 +--R ((a x y(x) + 4b x y(x))\|b + 2b y(x) )\|a y(x) + b +--R + +--R 5 3 +-+ 3 2 +--R (- a y(x) - 2b y(x) )\|b - 3a b x y(x) - 4b x y(x) +--R * +--R , +--R y (x) +--R +--R + +--R +-----------+ +--R 4 2 +-+ 2 2 | 2 +--R ((a y(x) + 2b y(x) )\|b + 3a b x y(x) + 4b x)\|a y(x) + b +--R + +--R 2 4 2 2 +-+ 4 2 2 +--R (- a x y(x) - 5a b x y(x) - 4b x)\|b - 2a b y(x) - 2b y(x) +--R / +--R +-----------+ +--R 2 2 | 2 2 4 2 2 +-+ +--R (3a b y(x) + 4b )\|a y(x) + b + (- a y(x) - 5a b y(x) - 4b )\|b +--R Type: Expression Integer +--E 29 + +--S 30 of 127 +ode210 := y(x)*D(y(x),x)+x*y(x)**2-4*x +--R +--R +--R , 2 +--R (30) y(x)y (x) + x y(x) - 4x +--R +--R Type: Expression Integer +--E 30 + +--S 31 of 127 +yx:=solve(ode210,y,x) +--R +--R +--R 2 +--R 2 x +--R (y(x) - 4)%e +--R (31) --------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 31 + +--S 32 of 127 +ode210expr := yx*D(yx,x)+x*yx**2-4*x +--R +--R +--R (32) +--R 2 2 2 2 +--R 3 x , 4 2 x +--R (2y(x) - 8y(x))(%e ) y (x) + (3x y(x) - 24x y(x) + 48x)(%e ) - 16x +--R +--R ------------------------------------------------------------------------ +--R 4 +--R Type: Expression Integer +--E 32 + +--S 33 of 127 +ode211 := y(x)*D(y(x),x)-x*exp(x/y(x)) +--R +--R +--R x +--R ---- +--R , y(x) +--R (33) y(x)y (x) - x %e +--R +--R Type: Expression Integer +--E 33 + +--S 34 of 127 +solve(ode211,y,x) +--R +--R +--R (34) "failed" +--R Type: Union("failed",...) +--E 34 + +--S 35 of 127 +ode212 := y(x)*D(y(x),x)+f(x**2+y(x)**2)*g(x)+x +--R +--R +--R , 2 2 +--R (35) y(x)y (x) + g(x)f(y(x) + x ) + x +--R +--R Type: Expression Integer +--E 35 + +--S 36 of 127 +solve(ode212,y,x) +--R +--R +--R (36) "failed" +--R Type: Union("failed",...) +--E 36 + +--S 37 of 127 +ode213 := (y(x)+1)*D(y(x),x)-y(x)-x +--R +--R +--R , +--R (37) (y(x) + 1)y (x) - y(x) - x +--R +--R Type: Expression Integer +--E 37 + +--S 38 of 127 +solve(ode213,y,x) +--R +--R +--R (38) "failed" +--R Type: Union("failed",...) +--E 38 + +--S 39 of 127 +ode214 := (y(x)+x-1)*D(y(x),x)-y(x)+2*x+3 +--R +--R +--R , +--R (39) (y(x) + x - 1)y (x) - y(x) + 2x + 3 +--R +--R Type: Expression Integer +--E 39 + +--S 40 of 127 +solve(ode214,y,x) +--R +--R +--R (40) "failed" +--R Type: Union("failed",...) +--E 40 + +--S 41 of 127 +ode215 := (y(x)+2*x-2)*D(y(x),x)-y(x)+x+1 +--R +--R +--R , +--R (41) (y(x) + 2x - 2)y (x) - y(x) + x + 1 +--R +--R Type: Expression Integer +--E 41 + +--S 42 of 127 +solve(ode215,y,x) +--R +--R +--R (42) "failed" +--R Type: Union("failed",...) +--E 42 + +--S 43 of 127 +ode216 := (y(x)-2*x+1)*D(y(x),x)+y(x)+x +--R +--R +--R , +--R (43) (y(x) - 2x + 1)y (x) + y(x) + x +--R +--R Type: Expression Integer +--E 43 + +--S 44 of 127 +solve(ode216,y,x) +--R +--R +--R (44) "failed" +--R Type: Union("failed",...) +--E 44 + +--S 45 of 127 +ode217 := (y(x)-x**2)*D(y(x),x)-x +--R +--R +--R 2 , +--R (45) (y(x) - x )y (x) - x +--R +--R Type: Expression Integer +--E 45 + +--S 46 of 127 +yx:=solve(ode217,y,x) +--R +--R +--R 2 2y(x) +--R (2y(x) - 2x - 1)%e +--R (46) ------------------------ +--R 4 +--R Type: Union(Expression Integer,...) +--E 46 + +--S 47 of 127 +ode217expr := (yx-x**2)*D(yx,x)-x +--R +--R +--R (47) +--R 2 2 4 2 2y(x) 2 +--R (2y(x) + (- 4x - 1)y(x) + 2x + x )(%e ) +--R + +--R 2 4 2y(x) +--R (- 4x y(x) + 4x )%e +--R * +--R , +--R y (x) +--R +--R + +--R 3 2y(x) 2 3 2y(x) +--R (- 2x y(x) + 2x + x)(%e ) + 4x %e - 4x +--R / +--R 4 +--R Type: Expression Integer +--E 47 + +--S 48 of 127 +ode218 := (y(x)-x**2)*D(y(x),x)+4*x*y(x) +--R +--R +--R 2 , +--R (48) (y(x) - x )y (x) + 4x y(x) +--R +--R Type: Expression Integer +--E 48 + +--S 49 of 127 +yx:=solve(ode218,y,x) +--R +--R +--R 2 +--R 2y(x) + 2x +--R (49) ----------- +--R +----+ +--R \|y(x) +--R Type: Union(Expression Integer,...) +--E 49 + +--S 50 of 127 +ode218expr := (yx-x**2)*D(yx,x)+4*x*yx +--R +--R +--R (50) +--R 2 4 +----+ 2 2 4 , +--R ((2y(x) - 2x )\|y(x) - x y(x) + x y(x))y (x) +--R +--R + +--R 2 3 +----+ 3 3 2 +--R (8x y(x) + 8x y(x))\|y(x) + 8x y(x) + 4x y(x) +--R / +--R 2 +----+ +--R y(x) \|y(x) +--R Type: Expression Integer +--E 50 + +--S 51 of 127 +ode219 := (y(x)+g(x))*D(y(x),x)-f2(x)*y(x)**2-f1(x)*y(x)-f0(x) +--R +--R +--R , 2 +--R (51) (y(x) + g(x))y (x) - f2(x)y(x) - f1(x)y(x) - f0(x) +--R +--R Type: Expression Integer +--E 51 + +--S 52 of 127 +solve(ode219,y,x) +--R +--R +--R (52) "failed" +--R Type: Union("failed",...) +--E 52 + +--S 53 of 127 +ode220 := 2*y(x)*D(y(x),x)-x*y(x)**2-x**3 +--R +--R +--R , 2 3 +--R (53) 2y(x)y (x) - x y(x) - x +--R +--R Type: Expression Integer +--E 53 + +--S 54 of 127 +yx:=solve(ode220,y,x) +--R +--R +--R 2 +--R x +--R - -- +--R 2 2 2 +--R (54) (y(x) + x + 2)%e +--R Type: Union(Expression Integer,...) +--E 54 + +--S 55 of 127 +ode220expr := 2*yx*D(yx,x)-x*yx**2-x**3 +--R +--R +--R (55) +--R 2 2 +--R x +--R - -- +--R 3 2 2 , +--R (4y(x) + (4x + 8)y(x))(%e ) y (x) +--R +--R + +--R 2 2 +--R x +--R - -- +--R 4 3 2 5 3 2 3 +--R (- 3x y(x) + (- 6x - 8x)y(x) - 3x - 8x - 4x)(%e ) - x +--R Type: Expression Integer +--E 55 + +--S 56 of 127 +ode221 := (2*y(x)+x+1)*D(y(x),x)-(2*y(x)+x-1) +--R +--R +--R , +--R (56) (2y(x) + x + 1)y (x) - 2y(x) - x + 1 +--R +--R Type: Expression Integer +--E 56 + +--S 57 of 127 +solve(ode221,y,x) +--R +--R +--R (57) "failed" +--R Type: Union("failed",...) +--E 57 + +--S 58 of 127 +ode222 := (2*y(x)+x+7)*D(y(x),x)-y(x)+2*x+4 +--R +--R +--R , +--R (58) (2y(x) + x + 7)y (x) - y(x) + 2x + 4 +--R +--R Type: Expression Integer +--E 58 + +--S 59 of 127 +solve(ode222,y,x) +--R +--R +--R (59) "failed" +--R Type: Union("failed",...) +--E 59 + +--S 60 of 127 +ode223 := (2*y(x)-x)*D(y(x),x)-y(x)-2*x +--R +--R +--R , +--R (60) (2y(x) - x)y (x) - y(x) - 2x +--R +--R Type: Expression Integer +--E 60 + +--S 61 of 127 +yx:=solve(ode223,y,x) +--R +--R +--R 2 2 +--R (61) y(x) - x y(x) - x +--R Type: Union(Expression Integer,...) +--E 61 + +--S 62 of 127 +ode223expr := (2*yx-x)*D(yx,x)-yx-2*x +--R +--R +--R (62) +--R 3 2 2 3 2 , 3 +--R (4y(x) - 6x y(x) + (- 2x - 2x)y(x) + 2x + x )y (x) - 2y(x) +--R +--R + +--R 2 2 3 2 +--R (- 2x - 1)y(x) + (6x + 2x)y(x) + 4x + 3x - 2x +--R Type: Expression Integer +--E 62 + +--S 63 of 127 +ode224 := (2*y(x)-6*x)*D(y(x),x)-y(x)+3*x+2 +--R +--R +--R , +--R (63) (2y(x) - 6x)y (x) - y(x) + 3x + 2 +--R +--R Type: Expression Integer +--E 63 + +--S 64 of 127 +solve(ode224,y,x) +--R +--R +--R (64) "failed" +--R Type: Union("failed",...) +--E 64 + +--S 65 of 127 +ode225 := (4*y(x)+2*x+3)*D(y(x),x)-2*y(x)-x-1 +--R +--R +--R , +--R (65) (4y(x) + 2x + 3)y (x) - 2y(x) - x - 1 +--R +--R Type: Expression Integer +--E 65 + +--S 66 of 127 +solve(ode225,y,x) +--R +--R +--R (66) "failed" +--R Type: Union("failed",...) +--E 66 + +--S 67 of 127 +ode226 := (4*y(x)-2*x-3)*D(y(x),x)+2*y(x)-x-1 +--R +--R +--R , +--R (67) (4y(x) - 2x - 3)y (x) + 2y(x) - x - 1 +--R +--R Type: Expression Integer +--E 67 + +--S 68 of 127 +solve(ode226,y,x) +--R +--R +--R (68) "failed" +--R Type: Union("failed",...) +--E 68 + +--S 69 of 127 +ode227 := (4*y(x)-3*x-5)*D(y(x),x)-3*y(x)+7*x+2 +--R +--R +--R , +--R (69) (4y(x) - 3x - 5)y (x) - 3y(x) + 7x + 2 +--R +--R Type: Expression Integer +--E 69 + +--S 70 of 127 +yx:=solve(ode227,y,x) +--R +--R +--R 2 2 +--R 4y(x) + (- 6x - 10)y(x) + 7x + 4x +--R (70) ----------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 70 + +--S 71 of 127 +ode227expr := (4*yx-3*x-5)*D(yx,x)-3*yx+7*x+2 +--R +--R +--R (71) +--R 3 2 2 3 +--R 64y(x) + (- 144x - 240)y(x) + (184x + 280x + 160)y(x) - 84x +--R + +--R 2 +--R - 170x - 20x + 50 +--R * +--R , +--R y (x) +--R +--R + +--R 3 2 2 3 2 +--R - 48y(x) + (184x + 140)y(x) + (- 252x - 340x - 20)y(x) + 196x + 105x +--R + +--R - 48x - 16 +--R / +--R 2 +--R Type: Expression Integer +--E 71 + +--S 72 of 127 +ode228 := (4*y(x)+11*x-11) *D(y(x),x)-25*y(x)-8*x+62 +--R +--R +--R , +--R (72) (4y(x) + 11x - 11)y (x) - 25y(x) - 8x + 62 +--R +--R Type: Expression Integer +--E 72 + +--S 73 of 127 +solve(ode228,y,x) +--R +--R +--R (73) "failed" +--R Type: Union("failed",...) +--E 73 + +--S 74 of 127 +ode229 := (12*y(x)-5*x-8)*D(y(x),x)-5*y(x)+2*x+3 +--R +--R +--R , +--R (74) (12y(x) - 5x - 8)y (x) - 5y(x) + 2x + 3 +--R +--R Type: Expression Integer +--E 74 + +--S 75 of 127 +yx:=solve(ode229,y,x) +--R +--R +--R 2 2 +--R (75) 6y(x) + (- 5x - 8)y(x) + x + 3x +--R Type: Union(Expression Integer,...) +--E 75 + +--S 76 of 127 +ode229expr := (12*yx-5*x-8)*D(yx,x)-5*yx+2*x+3 +--R +--R +--R (76) +--R 3 2 2 3 +--R 864y(x) + (- 1080x - 1728)y(x) + (444x + 1332x + 672)y(x) - 60x +--R + +--R 2 +--R - 251x - 208x + 64 +--R * +--R , +--R y (x) +--R +--R + +--R 3 2 2 3 2 +--R - 360y(x) + (444x + 666)y(x) + (- 180x - 502x - 208)y(x) + 24x + 93x +--R + +--R 64x - 21 +--R Type: Expression Integer +--E 76 + +--S 77 of 127 +ode230 := a*y(x)*D(y(x),x)+b*y(x)**2+f(x) +--R +--R +--R , 2 +--R (77) a y(x)y (x) + b y(x) + f(x) +--R +--R Type: Expression Integer +--E 77 + +--S 78 of 127 +solve(ode230,y,x) +--R +--R +--I 2%I b +--R x ----- +--R ++ 2 a +--I (78) | (b y(x) + f(%I))%e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 of 127 +ode231 := (a*y(x)+b*x+c)*D(y(x),x)+alpha*y(x)+beta*x+gamma +--R +--R +--R , +--R (79) (a y(x) + b x + c)y (x) + alpha y(x) + beta x + gamma +--R +--R Type: Expression Integer +--E 79 + +--S 80 of 127 +solve(ode231,y,x) +--R +--R +--R (80) "failed" +--R Type: Union("failed",...) +--E 80 + +--S 81 of 127 +ode232 := x*y(x)*D(y(x),x)+y(x)**2+x**2 +--R +--R +--R , 2 2 +--R (81) x y(x)y (x) + y(x) + x +--R +--R Type: Expression Integer +--E 81 + +--S 82 of 127 +yx:=solve(ode232,y,x) +--R +--R +--R 2 2 4 +--R 2x y(x) + x +--R (82) ------------- +--R 4 +--R Type: Union(Expression Integer,...) +--E 82 + +--S 83 of 127 +ode232expr := x*yx*D(yx,x)+yx**2+x**2 +--R +--R +--R 5 3 7 , 4 4 6 2 8 2 +--R (8x y(x) + 4x y(x))y (x) + 12x y(x) + 16x y(x) + 5x + 16x +--R +--R (83) -------------------------------------------------------------- +--R 16 +--R Type: Expression Integer +--E 83 + +--S 84 of 127 +ode233 := x*y(x)*D(y(x),x)-y(x)**2+a*x**3*cos(x) +--R +--R +--R , 3 2 +--R (84) x y(x)y (x) + a x cos(x) - y(x) +--R +--R Type: Expression Integer +--E 84 + +--S 85 of 127 +yx:=solve(ode233,y,x) +--R +--R +--R 2 2 +--R 2a x sin(x) + y(x) +--R (85) ------------------- +--R 2 +--R 2x +--R Type: Union(Expression Integer,...) +--E 85 + +--S 86 of 127 +ode233expr := x*yx*D(yx,x)-yx**2+a*x**3*cos(x) +--R +--R +--R (86) +--R 3 3 , 2 4 2 +--R (4a x y(x)sin(x) + 2x y(x) )y (x) - 4a x sin(x) +--R +--R + +--R 2 5 2 2 3 2 7 4 +--R (4a x cos(x) - 8a x y(x) )sin(x) + (2a x y(x) + 4a x )cos(x) - 3y(x) +--R / +--R 4 +--R 4x +--R Type: Expression Integer +--E 86 + +--S 87 of 127 +ode234 := x*y(x)*D(y(x),x)-y(x)**2+x*y(x)+x**3-2*x**2 +--R +--R +--R , 2 3 2 +--R (87) x y(x)y (x) - y(x) + x y(x) + x - 2x +--R +--R Type: Expression Integer +--E 87 + +--S 88 of 127 +solve(ode234,y,x) +--R +--R +--R (88) "failed" +--R Type: Union("failed",...) +--E 88 + +--S 89 of 127 +ode235 := (x*y(x)+a)*D(y(x),x)+b*y(x) +--R +--R +--R , +--R (89) (x y(x) + a)y (x) + b y(x) +--R +--R Type: Expression Integer +--E 89 + +--S 90 of 127 +yx:=solve(ode235,y,x) +--R +--R +--R y(x) +--R ---- +--R b y(x) +--R (90) b x %e + a Ei(----) +--R b +--R Type: Union(Expression Integer,...) +--E 90 + +--S 91 of 127 +ode235expr := (x*yx+a)*D(yx,x)+b*yx +--R +--R +--R (91) +--R y(x) 2 +--R ---- +--R 3 2 b +--R (b x y(x) + a b x )(%e ) +--R + +--R y(x) +--R ---- +--R 2 2 y(x) 2 b +--R ((a x y(x) + a x)Ei(----) + a x y(x) + a )%e +--R b +--R * +--R , +--R y (x) +--R +--R + +--R y(x) 2 y(x) +--R ---- ---- +--R 2 2 b y(x) 2 b +--R b x y(x)(%e ) + (a b x y(x)Ei(----) + (b x + a b)y(x))%e +--R b +--R + +--R y(x) +--R a b y(x)Ei(----) +--R b +--R / +--R y(x) +--R Type: Expression Integer +--E 91 + +--S 92 of 127 +ode236 := x*(y(x)+4)*D(y(x),x)-y(x)**2-2*y(x)-2*x +--R +--R +--R , 2 +--R (92) (x y(x) + 4x)y (x) - y(x) - 2y(x) - 2x +--R +--R Type: Expression Integer +--E 92 + +--S 93 of 127 +solve(ode236,y,x) +--R +--R +--R (93) "failed" +--R Type: Union("failed",...) +--E 93 + +--S 94 of 127 +ode237 := x*(y(x)+a)*D(y(x),x)+b*y(x)+c*x +--R +--R +--R , +--R (94) (x y(x) + a x)y (x) + b y(x) + c x +--R +--R Type: Expression Integer +--E 94 + +--S 95 of 127 +solve(ode237,y,x) +--R +--R +--R (95) "failed" +--R Type: Union("failed",...) +--E 95 + +--S 96 of 127 +ode238 := (x*(y(x)+x)+a)*D(y(x),x)-y(x)*(y(x)+x)-b +--R +--R +--R 2 , 2 +--R (96) (x y(x) + x + a)y (x) - y(x) - x y(x) - b +--R +--R Type: Expression Integer +--E 96 + +--S 97 of 127 +solve(ode238,y,x) +--R +--R +--R (97) "failed" +--R Type: Union("failed",...) +--E 97 + +--S 98 of 127 +ode239 := (x*y(x)-x**2)*D(y(x),x)+y(x)**2-3*x*y(x)-2*x**2 +--R +--R +--R 2 , 2 2 +--R (98) (x y(x) - x )y (x) + y(x) - 3x y(x) - 2x +--R +--R Type: Expression Integer +--E 98 + +--S 99 of 127 +yx:=solve(ode239,y,x) +--R +--R +--R 2 2 3 4 +--R x y(x) - 2x y(x) - x +--R (99) ---------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 99 + +--S 100 of 127 +ode239expr := (x*yx-x**2)*D(yx,x)+yx**2-3*x*yx-2*x**2 +--R +--R +--R (100) +--R 5 3 6 2 7 4 8 5 , 4 4 +--R (2x y(x) - 6x y(x) + (2x - 4x )y(x) + 2x + 4x )y (x) + 3x y(x) +--R +--R + +--R 5 3 6 3 2 7 4 8 5 2 +--R - 14x y(x) + (8x - 10x )y(x) + (18x + 24x )y(x) + 5x + 14x - 8x +--R / +--R 4 +--R Type: Expression Integer +--E 100 + +--S 101 of 127 +ode240 := 2*x*y(x)*D(y(x),x)-y(x)**2+a*x +--R +--R +--R , 2 +--R (101) 2x y(x)y (x) - y(x) + a x +--R +--R Type: Expression Integer +--E 101 + +--S 102 of 127 +yx:=solve(ode240,y,x) +--R +--R +--R 2 +--R a x log(x) + y(x) +--R (102) ------------------ +--R x +--R Type: Union(Expression Integer,...) +--E 102 + +--S 103 of 127 +ode240expr := 2*x*yx*D(yx,x)-yx**2+a*x +--R +--R +--R (103) +--R 2 3 , 2 2 2 +--R (4a x y(x)log(x) + 4x y(x) )y (x) - a x log(x) +--R +--R + +--R 2 2 2 4 2 3 +--R (- 4a x y(x) + 2a x )log(x) - 3y(x) + 2a x y(x) + a x +--R / +--R 2 +--R x +--R Type: Expression Integer +--E 103 + +--S 104 of 127 +ode241 := 2*x*y(x)*D(y(x),x)-y(x)**2+a*x**2 +--R +--R +--R , 2 2 +--R (104) 2x y(x)y (x) - y(x) + a x +--R +--R Type: Expression Integer +--E 104 + +--S 105 of 127 +yx:=solve(ode241,y,x) +--R +--R +--R 2 2 +--R y(x) + a x +--R (105) ------------ +--R x +--R Type: Union(Expression Integer,...) +--E 105 + +--S 106 of 127 +ode241expr := 2*x*yx*D(yx,x)-yx**2+a*x**2 +--R +--R +--R 3 3 , 4 2 2 2 4 +--R (4x y(x) + 4a x y(x))y (x) - 3y(x) - 2a x y(x) + (a + a)x +--R +--R (106) -------------------------------------------------------------- +--R 2 +--R x +--R Type: Expression Integer +--E 106 + +--S 107 of 127 +ode242 := 2*x*y(x)*D(y(x),x)+2*y(x)**2+1 +--R +--R +--R , 2 +--R (107) 2x y(x)y (x) + 2y(x) + 1 +--R +--R Type: Expression Integer +--E 107 + +--S 108 of 127 +yx:=solve(ode242,y,x) +--R +--R +--R 2 2 2 +--R 2x y(x) + x +--R (108) ------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 108 + +--S 109 of 127 +ode242expr := 2*x*yx*D(yx,x)+2*yx**2+1 +--R +--R +--R 5 3 5 , 4 4 4 2 4 +--R (8x y(x) + 4x y(x))y (x) + 12x y(x) + 12x y(x) + 3x + 2 +--R +--R (109) ----------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 109 + +--S 110 of 127 +ode243 := x*(2*y(x)+x-1)*D(y(x),x)-y(x)*(y(x)+2*x+1) +--R +--R +--R 2 , 2 +--R (110) (2x y(x) + x - x)y (x) - y(x) + (- 2x - 1)y(x) +--R +--R Type: Expression Integer +--E 110 + +--S 111 of 127 +solve(ode243,y,x) +--R +--R +--R (111) "failed" +--R Type: Union("failed",...) +--E 111 + +--S 112 of 127 +ode244 := x*(2*y(x)-x-1)*D(y(x),x)+y(x)*(2*x-y(x)-1) +--R +--R +--R 2 , 2 +--R (112) (2x y(x) - x - x)y (x) - y(x) + (2x - 1)y(x) +--R +--R Type: Expression Integer +--E 112 + +--S 113 of 127 +solve(ode244,y,x) +--R +--R +--R (113) "failed" +--R Type: Union("failed",...) +--E 113 + +--S 114 of 127 +ode245 := (2*x*y(x)+4*x**3)*D(y(x),x)+y(x)**2+112*x**2*y(x) +--R +--R +--R 3 , 2 2 +--R (114) (2x y(x) + 4x )y (x) + y(x) + 112x y(x) +--R +--R Type: Expression Integer +--E 114 + +--S 115 of 127 +solve(ode245,y,x) +--R +--R +--R (115) "failed" +--R Type: Union("failed",...) +--E 115 + +--S 116 of 127 +ode246 := x*(3*y(x)+2*x)*D(y(x),x)+3*(y(x)+x)**2 +--R +--R +--R 2 , 2 2 +--R (116) (3x y(x) + 2x )y (x) + 3y(x) + 6x y(x) + 3x +--R +--R Type: Expression Integer +--E 116 + +--S 117 of 127 +yx:=solve(ode246,y,x) +--R +--R +--R 2 2 3 4 +--R 6x y(x) + 8x y(x) + 3x +--R (117) ------------------------ +--R 4 +--R Type: Union(Expression Integer,...) +--E 117 + +--S 118 of 127 +ode246expr := x*(3*yx+2*x)*D(yx,x)+3*(yx+x)**2 +--R +--R +--R (118) +--R 5 3 6 2 7 4 8 5 , +--R (216x y(x) + 432x y(x) + (300x + 96x )y(x) + 72x + 64x )y (x) +--R +--R + +--R 4 4 5 3 6 3 2 7 4 +--R 324x y(x) + 1008x y(x) + (1200x + 240x )y(x) + (648x + 384x )y(x) +--R + +--R 8 5 2 +--R 135x + 168x + 48x +--R / +--R 16 +--R Type: Expression Integer +--E 118 + +--S 119 of 127 +ode247 := (3*x+2)*(y(x)-2*x-1)*D(y(x),x)-y(x)**2+x*y(x)-7*x**2-9*x-3 +--R +--R +--R 2 , 2 2 +--R (119) ((3x + 2)y(x) - 6x - 7x - 2)y (x) - y(x) + x y(x) - 7x - 9x - 3 +--R +--R Type: Expression Integer +--E 119 + +--S 120 of 127 +solve(ode247,y,x) +--R +--R +--R (120) "failed" +--R Type: Union("failed",...) +--E 120 + +--S 121 of 127 +ode248 := (6*x*y(x)+x**2+3)*D(y(x),x)+3*y(x)**2+2*x*y(x)+2*x +--R +--R +--R 2 , 2 +--R (121) (6x y(x) + x + 3)y (x) + 3y(x) + 2x y(x) + 2x +--R +--R Type: Expression Integer +--E 121 + +--S 122 of 127 +yx:=solve(ode248,y,x) +--R +--R +--R 2 2 2 +--R (122) 3x y(x) + (x + 3)y(x) + x +--R Type: Union(Expression Integer,...) +--E 122 + +--S 123 of 127 +ode248expr := (6*x*yx+x**2+3)*D(yx,x)+3*yx**2+2*x*yx+2*x +--R +--R +--R (123) +--R 3 3 4 2 2 5 4 3 5 +--R 108x y(x) + (54x + 162x )y(x) + (6x + 36x + 42x + 72x)y(x) + 6x +--R + +--R 4 3 2 +--R x + 18x + 6x + 9 +--R * +--R , +--R y (x) +--R +--R + +--R 2 4 3 3 4 3 2 2 +--R 81x y(x) + (72x + 108x)y(x) + (15x + 72x + 63x + 36)y(x) +--R + +--R 4 3 2 4 3 +--R (30x + 4x + 54x + 12x)y(x) + 15x + 4x + 8x +--R Type: Expression Integer +--E 123 + +--S 124 of 127 +ode249 := (a*x*y(x)+b*x**n)*D(y(x),x)+alpha*y(x)**3+beta*y(x)**2 +--R +--R +--R n , 3 2 +--R (124) (b x + a x y(x))y (x) + alpha y(x) + beta y(x) +--R +--R Type: Expression Integer +--E 124 + +--S 125 of 127 +solve(ode249,y,x) +--R +--R +--R (125) "failed" +--R Type: Union("failed",...) +--E 125 + +--S 126 of 127 +ode250 := (B*x*y(x)+A*x**2+a*x+b*y(x)+c)*D(y(x),x)-B*g(x)**2+_ + A*x*y(x)+alpha*x+beta*y(x)+gamma +--R +--R +--R (126) +--R 2 , 2 +--R ((B x + b)y(x) + A x + a x + c)y (x) + (A x + beta)y(x) - B g(x) +--R +--R + +--R alpha x + gamma +--R Type: Expression Integer +--E 126 + +--S 127 of 127 +solve(ode250,y,x) +--R +--R +--R (127) "failed" +--R Type: Union("failed",...) +--E 127 + +)spool +)lisp (bye) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} {\bf http://www.cs.uwaterloo.ca/$\tilde{}$ecterrab/odetools.html} +\end{thebibliography} +\end{document} +