diff --git a/changelog b/changelog index 666bd42..916c822 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,5 @@ +20071005 tpd src/input/Makefile kamke5.input regression test added +20071005 tpd src/input/kamke5.input ODE regression test added 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 diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index b803938..1d2626f 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -323,7 +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 \ + kamke4.regress kamke5.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 \ @@ -564,6 +564,7 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input ${OUT}/algfacob.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}/kamke4.input \ + ${OUT}/kamke5.input \ ${OUT}/kernel.input ${OUT}/knot.input \ ${OUT}/kovacic.input ${OUT}/kuipers.input \ ${OUT}/laplace.input ${OUT}/leg.input ${OUT}/lexp.input \ @@ -831,7 +832,7 @@ 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}/kamke4.input.dvi ${DOC}/kamke5.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/kamke5.input.pamphlet b/src/input/kamke5.input.pamphlet new file mode 100644 index 0000000..34a8ee0 --- /dev/null +++ b/src/input/kamke5.input.pamphlet @@ -0,0 +1,1634 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input kamke5.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This is the 251-300 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 kamke5.output +)set break resume +)set mes auto off +)clear all + +--S 1 of 130 +y:=operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 1 + +--S 2 of 130 +f:=operator 'f +--R +--R +--R (2) f +--R Type: BasicOperator +--E 2 + +--S 3 of 130 +f0:=operator 'f0 +--R +--R +--R (3) f0 +--R Type: BasicOperator +--E 3 + +--S 4 of 130 +f1:=operator 'f1 +--R +--R +--R (4) f1 +--R Type: BasicOperator +--E 4 + +--S 5 of 130 +f2:=operator 'f2 +--R +--R +--R (5) f2 +--R Type: BasicOperator +--E 5 + +--S 6 of 130 +f3:=operator 'f3 +--R +--R +--R (6) f3 +--R Type: BasicOperator +--E 6 + +--S 7 of 130 +g:=operator 'g +--R +--R +--R (7) g +--R Type: BasicOperator +--E 7 + +--S 8 of 130 +g0:=operator 'g0 +--R +--R +--R (8) g0 +--R Type: BasicOperator +--E 8 + +--S 9 of 130 +g1:=operator 'g1 +--R +--R +--R (9) g1 +--R Type: BasicOperator +--E 9 + +--S 10 of 130 +h:=operator 'h +--R +--R +--R (10) h +--R Type: BasicOperator +--E 10 + +--S 11 of 130 +ode251 := (x**2*y(x)-1)*D(y(x),x)+x*y(x)**2-1 +--R +--R +--R 2 , 2 +--R (11) (x y(x) - 1)y (x) + x y(x) - 1 +--R +--R Type: Expression Integer +--E 11 + +--S 12 of 130 +yx:=solve(ode251,y,x) +--R +--R +--R 2 2 +--R x y(x) - 2y(x) - 2x +--R (12) -------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 12 + +--S 13 of 130 +ode251expr := (x**2*yx-1)*D(yx,x)+x*yx**2-1 +--R +--R +--R (13) +--R 6 3 4 2 5 3 , 5 4 3 3 +--R (2x y(x) - 6x y(x) - 4x y(x) + 4x + 4)y (x) + 3x y(x) - 8x y(x) +--R +--R + +--R 4 2 2 3 +--R - 10x y(x) + 12x y(x) + 8x +--R / +--R 4 +--R Type: Expression Integer +--E 13 + +--S 14 of 130 +ode252 := (x**2*y(x)-1)*D(y(x),x)-(x*y(x)**2-1) +--R +--R +--R 2 , 2 +--R (14) (x y(x) - 1)y (x) - x y(x) + 1 +--R +--R Type: Expression Integer +--E 14 + +--S 15 of 130 +solve(ode252,y,x) +--R +--R +--R (15) "failed" +--R Type: Union("failed",...) +--E 15 + +--S 16 of 130 +ode253 := (x**2*y(x)-1)*D(y(x),x)+8*(x*y(x)**2-1) +--R +--R +--R 2 , 2 +--R (16) (x y(x) - 1)y (x) + 8x y(x) - 8 +--R +--R Type: Expression Integer +--E 16 + +--S 17 of 130 +solve(ode253,y,x) +--R +--R +--R (17) "failed" +--R Type: Union("failed",...) +--E 17 + +--S 18 of 130 +ode254 := x*(x*y(x)-2)*D(y(x),x)+x**2*y(x)**3+x*y(x)**2-2*y(x) +--R +--R +--R 2 , 2 3 2 +--R (18) (x y(x) - 2x)y (x) + x y(x) + x y(x) - 2y(x) +--R +--R Type: Expression Integer +--E 18 + +--S 19 of 130 +solve(ode254,y,x) +--R +--R +--R (19) "failed" +--R Type: Union("failed",...) +--E 19 + +--S 20 of 130 +ode255 := x*(x*y(x)-3)*D(y(x),x)+x*y(x)**2-y(x) +--R +--R +--R 2 , 2 +--R (20) (x y(x) - 3x)y (x) + x y(x) - y(x) +--R +--R Type: Expression Integer +--E 20 + +--S 21 of 130 +solve(ode255,y,x) +--R +--R +--R (21) "failed" +--R Type: Union("failed",...) +--E 21 + +--S 22 of 130 +ode256 := x**2*(y(x)-1)*D(y(x),x)+(x-1)*y(x) +--R +--R +--R 2 2 , +--R (22) (x y(x) - x )y (x) + (x - 1)y(x) +--R +--R Type: Expression Integer +--E 22 + +--S 23 of 130 +solve(ode256,y,x) +--R +--R +--R (23) "failed" +--R Type: Union("failed",...) +--E 23 + +--S 24 of 130 +ode257 := x*(x*y(x)+x**4-1)*D(y(x),x)-y(x)*(x*y(x)-x**4-1) +--R +--R +--R 2 5 , 2 4 +--R (24) (x y(x) + x - x)y (x) - x y(x) + (x + 1)y(x) +--R +--R Type: Expression Integer +--E 24 + +--S 25 of 130 +solve(ode257,y,x) +--R +--R +--R (25) "failed" +--R Type: Union("failed",...) +--E 25 + +--S 26 of 130 +ode258 := 2*x**2*y(x)*D(y(x),x)+y(x)**2-2*x**3-x**2 +--R +--R +--R 2 , 2 3 2 +--R (26) 2x y(x)y (x) + y(x) - 2x - x +--R +--R Type: Expression Integer +--E 26 + +--S 27 of 130 +yx:=solve(ode258,y,x) +--R +--R +--R 1 +--R - - +--R 2 2 x +--R (27) (y(x) - x )%e +--R Type: Union(Expression Integer,...) +--E 27 + +--S 28 of 130 +ode258expr := 2*x**2*yx*D(yx,x)+yx**2-2*x**3-x**2 +--R +--R +--R (28) +--R 1 2 +--R - - +--R 2 3 4 x , +--R (4x y(x) - 4x y(x))(%e ) y (x) +--R +--R + +--R 1 2 +--R - - +--R 4 3 2 2 5 4 x 3 2 +--R (3y(x) + (- 4x - 6x )y(x) + 4x + 3x )(%e ) - 2x - x +--R Type: Expression Integer +--E 28 + +--S 29 of 130 +ode259 := 2*x**2*y(x)*D(y(x),x)-y(x)**2-x**2*exp(x-1/x) +--R +--R +--R 2 +--R x - 1 +--R ------ +--R 2 , 2 x 2 +--R (29) 2x y(x)y (x) - x %e - y(x) +--R +--R Type: Expression Integer +--E 29 + +--S 30 of 130 +yx:=solve(ode259,y,x) +--R +--R +--R 2 +--R 1 x - 1 1 +--R - ------ - +--R x x 2 x +--R (30) - %e %e + y(x) %e +--R Type: Union(Expression Integer,...) +--E 30 + +--S 31 of 130 +ode259expr := 2*x**2*yx*D(yx,x)-yx**2-x**2*exp(x-1/x) +--R +--R +--R (31) +--R 2 +--R 1 2 x - 1 1 2 +--R - ------ - +--R 2 x x 2 3 x , +--R (- 4x y(x)(%e ) %e + 4x y(x) (%e ) )y (x) +--R +--R + +--R 2 2 2 +--R 1 2 x - 1 1 2 x - 1 +--R - ------ - ------ +--R 2 x x 2 2 x 2 x +--R (2x - 1)(%e ) (%e ) + ((- 2x + 4)y(x) (%e ) - x )%e +--R + +--R 1 2 +--R - +--R 4 x +--R - 3y(x) (%e ) +--R Type: Expression Integer +--E 31 + +--S 32 of 130 +ode260 := (2*x**2*y(x)+x)*D(y(x),x)-x**2*y(x)**3+2*x*y(x)**2+y(x) +--R +--R +--R 2 , 2 3 2 +--R (32) (2x y(x) + x)y (x) - x y(x) + 2x y(x) + y(x) +--R +--R Type: Expression Integer +--E 32 + +--S 33 of 130 +solve(ode260,y,x) +--R +--R +--R (33) "failed" +--R Type: Union("failed",...) +--E 33 + +--S 34 of 130 +ode261 := (2*x**2*y(x)-x)*D(y(x),x)-2*x*y(x)**2-y(x) +--R +--R +--R 2 , 2 +--R (34) (2x y(x) - x)y (x) - 2x y(x) - y(x) +--R +--R Type: Expression Integer +--E 34 + +--S 35 of 130 +solve(ode261,y,x) +--R +--R +--R (35) "failed" +--R Type: Union("failed",...) +--E 35 + +--S 36 of 130 +ode262 := (2*x**2*y(x)-x**3)*D(y(x),x)+y(x)**3-4*x*y(x)**2+2*x**3 +--R +--R +--R 2 3 , 3 2 3 +--R (36) (2x y(x) - x )y (x) + y(x) - 4x y(x) + 2x +--R +--R Type: Expression Integer +--E 36 + +--S 37 of 130 +solve(ode262,y,x) +--R +--R +--R (37) "failed" +--R Type: Union("failed",...) +--E 37 + +--S 38 of 130 +ode263 := 2*x**3+y(x)*D(y(x),x)+3*x**2*y(x)**2+7 +--R +--R +--R , 2 2 3 +--R (38) y(x)y (x) + 3x y(x) + 2x + 7 +--R +--R Type: Expression Integer +--E 38 + +--S 39 of 130 +solve(ode263,y,x) +--R +--R +--R x 3 +--I ++ 2 2 3 2%K +--I (39) | (3%K y(x) + 2%K + 7)%e d%K +--R ++ +--R Type: Union(Expression Integer,...) +--E 39 + +--S 40 of 130 +ode264 := 2*x*(x**3*y(x)+1)*D(y(x),x)+(3*x**3*y(x)-1)*y(x) +--R +--R +--R 4 , 3 2 +--R (40) (2x y(x) + 2x)y (x) + 3x y(x) - y(x) +--R +--R Type: Expression Integer +--E 40 + +--S 41 of 130 +solve(ode264,y,x) +--R +--R +--R (41) "failed" +--R Type: Union("failed",...) +--E 41 + +--S 42 of 130 +ode265 := (x**(n*(n+1))*y(x)-1)*D(y(x),x)+2*(n+1)**2*x**(n-1)_ + *(x**(n**2)*y(x)**2-1) +--R +--R +--R (42) +--R 2 2 +--R n + n , 2 2 n - 1 n +--R (y(x)x - 1)y (x) + (2n + 4n + 2)y(x) x x +--R +--R + +--R 2 n - 1 +--R (- 2n - 4n - 2)x +--R Type: Expression Integer +--E 42 + +--S 43 of 130 +solve(ode265,y,x) +--R +--R +--R (43) "failed" +--R Type: Union("failed",...) +--E 43 + +--S 44 of 130 +ode266 := (y(x)-x)*sqrt(x**2+1)*D(y(x),x)-a*sqrt((y(x)**2+1)**3) +--R +--R +--R +------+ +---------------------------+ +--R | 2 , | 6 4 2 +--R (44) (y(x) - x)\|x + 1 y (x) - a\|y(x) + 3y(x) + 3y(x) + 1 +--R +--R Type: Expression Integer +--E 44 + +--S 45 of 130 +solve(ode266,y,x) +--R +--R +--R (45) "failed" +--R Type: Union("failed",...) +--E 45 + +--S 46 of 130 +ode267 := y(x)*D(y(x),x)*sin(x)**2+y(x)**2*cos(x)*sin(x)-1 +--R +--R +--R 2 , 2 +--R (46) y(x)sin(x) y (x) + y(x) cos(x)sin(x) - 1 +--R +--R Type: Expression Integer +--E 46 + +--S 47 of 130 +yx:=solve(ode267,y,x) +--R +--R +--R 2 2 +--R y(x) sin(x) - 2x +--R (47) ----------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 47 + +--S 48 of 130 +ode267expr := yx*D(yx,x)*sin(x)**2+yx**2*cos(x)*sin(x)-1 +--R +--R +--R (48) +--R 3 6 4 , 4 5 +--R (2y(x) sin(x) - 4x y(x)sin(x) )y (x) + 3y(x) cos(x)sin(x) +--R +--R + +--R 2 4 2 3 2 2 +--R - 2y(x) sin(x) - 8x y(x) cos(x)sin(x) + 4x sin(x) + 4x cos(x)sin(x) - 4 +--R / +--R 4 +--R Type: Expression Integer +--E 48 + +--S 49 of 130 +ode268 := f(x)*y(x)*D(y(x),x)+g(x)*y(x)**2+h(x) +--R +--R +--R , 2 +--R (49) f(x)y(x)y (x) + g(x)y(x) + h(x) +--R +--R Type: Expression Integer +--E 49 + +--S 50 of 130 +solve(ode268,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 50 + +--S 51 of 130 +ode269 := (g1(x)*y(x)+g0(x))*D(y(x),x)-f1(x)*y(x)-_ + f2(x)*y(x)**2-f3(x)*y(x)**3-f0(x) +--R +--R +--R (50) +--R , 3 2 +--R (g1(x)y(x) + g0(x))y (x) - f3(x)y(x) - f2(x)y(x) - f1(x)y(x) - f0(x) +--R +--R Type: Expression Integer +--E 51 + +--S 52 of 130 +solve(ode269,y,x) +--R +--R +--R (51) "failed" +--R Type: Union("failed",...) +--E 52 + +--S 53 of 130 +ode270 := (y(x)**2-x)*D(y(x),x)-y(x)+x**2 +--R +--R +--R 2 , 2 +--R (52) (y(x) - x)y (x) - y(x) + x +--R +--R Type: Expression Integer +--E 53 + +--S 54 of 130 +yx:=solve(ode270,y,x) +--R +--R +--R 3 3 +--R y(x) - 3x y(x) + x +--R (53) -------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 54 + +--S 55 of 130 +ode270expr := (yx**2-x)*D(yx,x)-yx+x**2 +--R +--R +--R (54) +--R 8 6 3 5 2 4 4 3 +--R y(x) - 7x y(x) + 2x y(x) + 15x y(x) - 8x y(x) +--R + +--R 6 3 2 5 7 2 +--R (x - 9x - 9x)y(x) + 6x y(x) - x + 9x +--R * +--R , +--R y (x) +--R +--R + +--R 7 2 6 5 3 4 5 2 3 +--R - y(x) + x y(x) + 6x y(x) - 8x y(x) + (2x - 9x - 3)y(x) +--R + +--R 4 2 6 8 3 2 +--R 15x y(x) + (- 7x + 18x)y(x) + x - 12x + 9x +--R / +--R 9 +--R Type: Expression Integer +--E 55 + +--S 56 of 130 +ode271 := (y(x)**2+x**2)*D(y(x),x)+2*x*(y(x)+2*x) +--R +--R +--R 2 2 , 2 +--R (55) (y(x) + x )y (x) + 2x y(x) + 4x +--R +--R Type: Expression Integer +--E 56 + +--S 57 of 130 +yx:=solve(ode271,y,x) +--R +--R +--R 3 2 3 +--R y(x) + 3x y(x) + 4x +--R (56) --------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 57 + +--S 58 of 130 +ode271expr := (yx**2+x**2)*D(yx,x)+2*x*(yx+2*x) +--R +--R +--R (57) +--R 8 2 6 3 5 4 4 5 3 +--R y(x) + 7x y(x) + 8x y(x) + 15x y(x) + 32x y(x) +--R + +--R 6 2 2 7 8 4 +--R (25x + 9x )y(x) + 24x y(x) + 16x + 9x +--R * +--R , +--R y (x) +--R +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 2x y(x) + 4x y(x) + 12x y(x) + 40x y(x) + (50x + 6x)y(x) +--R + +--R 6 2 7 3 8 4 2 +--R 84x y(x) + (128x + 36x )y(x) + 64x + 60x + 36x +--R / +--R 9 +--R Type: Expression Integer +--E 58 + +--S 59 of 130 +ode272 := (y(x)**2+x**2)*D(y(x),x)-y(x)**2 +--R +--R +--R 2 2 , 2 +--R (58) (y(x) + x )y (x) - y(x) +--R +--R Type: Expression Integer +--E 59 + +--S 60 of 130 +solve(ode272,y,x) +--R +--R +--R (59) "failed" +--R Type: Union("failed",...) +--E 60 + +--S 61 of 130 +ode273 := (y(x)**2+x**2+a)*D(y(x),x)+2*x*y(x) +--R +--R +--R 2 2 , +--R (60) (y(x) + x + a)y (x) + 2x y(x) +--R +--R Type: Expression Integer +--E 61 + +--S 62 of 130 +yx:=solve(ode273,y,x) +--R +--R +--R 3 2 +--R y(x) + (3x + 3a)y(x) +--R (61) ---------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 62 + +--S 63 of 130 +ode273expr := (yx**2+x**2+a)*D(yx,x)+2*x*yx +--R +--R +--R (62) +--R 8 2 6 4 2 2 4 +--R y(x) + (7x + 7a)y(x) + (15x + 30a x + 15a )y(x) +--R + +--R 6 4 2 2 3 2 4 2 2 +--R (9x + 27a x + (27a + 9)x + 9a + 9a)y(x) + 9x + 18a x + 9a +--R * +--R , +--R y (x) +--R +--R + +--R 7 3 5 5 3 2 3 +--R 2x y(x) + (12x + 12a x)y(x) + (18x + 36a x + (18a + 6)x)y(x) +--R + +--R 3 +--R (36x + 36a x)y(x) +--R / +--R 9 +--R Type: Expression Integer +--E 63 + +--S 64 of 130 +ode274 := (y(x)**2+x**2+a)*D(y(x),x)+2*x*y(x)+x**2+b +--R +--R +--R 2 2 , 2 +--R (63) (y(x) + x + a)y (x) + 2x y(x) + x + b +--R +--R Type: Expression Integer +--E 64 + +--S 65 of 130 +yx:=solve(ode274,y,x) +--R +--R +--R 3 2 3 +--R y(x) + (3x + 3a)y(x) + x + 3b x +--R (64) ---------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 65 + +--S 66 of 130 +ode274expr := (yx**2+x**2+a)*D(yx,x)+2*x*yx+x**2+b +--R +--R +--R (65) +--R 8 2 6 3 5 +--R y(x) + (7x + 7a)y(x) + (2x + 6b x)y(x) +--R + +--R 4 2 2 4 5 3 3 +--R (15x + 30a x + 15a )y(x) + (8x + (24b + 8a)x + 24a b x)y(x) +--R + +--R 6 4 2 2 2 3 2 +--R (10x + (6b + 27a)x + (9b + 27a + 9)x + 9a + 9a)y(x) +--R + +--R 7 5 2 3 2 8 +--R (6x + (18b + 12a)x + (36a b + 6a )x + 18a b x)y(x) + x +--R + +--R 6 2 4 2 2 2 +--R (6b + a)x + (9b + 6a b + 9)x + (9a b + 18a)x + 9a +--R * +--R , +--R y (x) +--R +--R + +--R 7 2 6 3 5 +--R 2x y(x) + (x + b)y(x) + (12x + 12a x)y(x) +--R + +--R 4 2 4 +--R (10x + (18b + 6a)x + 6a b)y(x) +--R + +--R 5 3 2 2 3 +--R (20x + (8b + 36a)x + (6b + 18a + 6)x)y(x) +--R + +--R 6 4 2 2 2 2 +--R (21x + (45b + 30a)x + (54a b + 9a )x + 9a b)y(x) +--R + +--R 7 5 2 3 2 8 +--R (8x + (36b + 6a)x + (36b + 24a b + 36)x + (18a b + 36a)x)y(x) + x +--R + +--R 6 2 4 3 2 +--R 7b x + (15b + 15)x + (9b + 27b + 9a + 9)x + (9a + 9)b +--R / +--R 9 +--R Type: Expression Integer +--E 66 + +--S 67 of 130 +ode275 := (y(x)**2+x**2+x)*D(y(x),x)-y(x) +--R +--R +--R 2 2 , +--R (66) (y(x) + x + x)y (x) - y(x) +--R +--R Type: Expression Integer +--E 67 + +--S 68 of 130 +solve(ode275,y,x) +--R +--R +--R (67) "failed" +--R Type: Union("failed",...) +--E 68 + +--S 69 of 130 +ode276 := (y(x)**2-x**2)*D(y(x),x)+2*x*y(x) +--R +--R +--R 2 2 , +--R (68) (y(x) - x )y (x) + 2x y(x) +--R +--R Type: Expression Integer +--E 69 + +--S 70 of 130 +yx:=solve(ode276,y,x) +--R +--R +--R 2 2 +--R y(x) + x +--R (69) ---------- +--R y(x) +--R Type: Union(Expression Integer,...) +--E 70 + +--S 71 of 130 +ode276expr := (yx**2-x**2)*D(yx,x)+2*x*yx +--R +--R +--R 6 6 , 5 3 3 5 +--R (y(x) - x )y (x) + 4x y(x) + 4x y(x) + 2x y(x) +--R +--R (70) ------------------------------------------------- +--R 4 +--R y(x) +--R Type: Expression Integer +--E 71 + +--S 72 of 130 +ode277 := (y(x)**2+x**4)*D(y(x),x)-4*x**3*y(x) +--R +--R +--R 2 4 , 3 +--R (71) (y(x) + x )y (x) - 4x y(x) +--R +--R Type: Expression Integer +--E 72 + +--S 73 of 130 +yx:=solve(ode277,y,x) +--R +--R +--R 2 4 +--R y(x) - x +--R (72) ---------- +--R y(x) +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 130 +ode277expr := (yx**2+x**4)*D(yx,x)-4*x**3*yx +--R +--R +--R 6 12 , 3 5 7 3 11 +--R (y(x) + x )y (x) - 8x y(x) + 8x y(x) - 4x y(x) +--R +--R (73) --------------------------------------------------- +--R 4 +--R y(x) +--R Type: Expression Integer +--E 74 + +--S 75 of 130 +ode278 := (y(x)**2+4*sin(x))*D(y(x),x)-cos(x) +--R +--R +--R 2 , +--R (74) (4sin(x) + y(x) )y (x) - cos(x) +--R +--R Type: Expression Integer +--E 75 + +--S 76 of 130 +yx:=solve(ode278,y,x) +--R +--R +--R 2 - 4y(x) +--R (- 32sin(x) - 8y(x) - 4y(x) - 1)%e +--R (75) ------------------------------------------ +--R 32 +--R Type: Union(Expression Integer,...) +--E 76 + +--S 77 of 130 +ode278expr := (yx**2+4*sin(x))*D(yx,x)-cos(x) +--R +--R +--R (76) +--R 3 2 2 +--R 4096sin(x) + (3072y(x) + 1024y(x) + 256)sin(x) +--R + +--R 4 3 2 6 +--R (768y(x) + 512y(x) + 192y(x) + 32y(x) + 4)sin(x) + 64y(x) +--R + +--R 5 4 3 2 +--R 64y(x) + 32y(x) + 8y(x) + y(x) +--R * +--R - 4y(x) 3 +--R (%e ) +--R + +--R 2 2 - 4y(x) +--R (16384sin(x) + 4096y(x) sin(x))%e +--R * +--R , +--R y (x) +--R +--R + +--R 2 2 +--R - 1024cos(x)sin(x) + (- 512y(x) - 256y(x) - 64)cos(x)sin(x) +--R + +--R 4 3 2 +--R (- 64y(x) - 64y(x) - 32y(x) - 8y(x) - 1)cos(x) +--R * +--R - 4y(x) 3 +--R (%e ) +--R + +--R - 4y(x) +--R - 4096cos(x)sin(x)%e - 1024cos(x) +--R / +--R 1024 +--R Type: Expression Integer +--E 77 + +--S 78 of 130 +ode279 := (y(x)**2+2*y(x)+x)*D(y(x),x)+(y(x)+x)**2*y(x)**2+y(x)*(y(x)+1) +--R +--R +--R 2 , 4 3 2 2 +--R (77) (y(x) + 2y(x) + x)y (x) + y(x) + 2x y(x) + (x + 1)y(x) + y(x) +--R +--R Type: Expression Integer +--E 78 + +--S 79 of 130 +solve(ode279,y,x) +--R +--R +--R (78) "failed" +--R Type: Union("failed",...) +--E 79 + +--S 80 of 130 +ode280 := (y(x)+x)**2*D(y(x),x)-a**2 +--R +--R +--R 2 2 , 2 +--R (79) (y(x) + 2x y(x) + x )y (x) - a +--R +--R Type: Expression Integer +--E 80 + +--S 81 of 130 +solve(ode280,y,x) +--R +--R +--R (80) "failed" +--R Type: Union("failed",...) +--E 81 + +--S 82 of 130 +ode281 := (y(x)**2+2*x*y(x)-x**2)*D(y(x),x)-_ + y(x)**2+2*x*y(x)+x**2 +--R +--R +--R 2 2 , 2 2 +--R (81) (y(x) + 2x y(x) - x )y (x) - y(x) + 2x y(x) + x +--R +--R Type: Expression Integer +--E 82 + +--S 83 of 130 +solve(ode281,y,x) +--R +--R +--R (82) "failed" +--R Type: Union("failed",...) +--E 83 + +--S 84 of 130 +ode282 := (y(x)+3*x-1)**2*D(y(x),x)-(2*y(x)-1)*(4*y(x)+6*x-3) +--R +--R +--R (83) +--R 2 2 , 2 +--R (y(x) + (6x - 2)y(x) + 9x - 6x + 1)y (x) - 8y(x) + (- 12x + 10)y(x) + 6x +--R +--R + +--R - 3 +--R Type: Expression Integer +--E 84 + +--S 85 of 130 +solve(ode282,y,x) +--R +--R +--R (84) "failed" +--R Type: Union("failed",...) +--E 85 + +--S 86 of 130 +ode283 := 3*(y(x)**2-x**2)*D(y(x),x)+2*y(x)**3-6*x*(x+1)*y(x)-3*exp(x) +--R +--R +--R 2 2 , x 3 2 +--R (85) (3y(x) - 3x )y (x) - 3%e + 2y(x) + (- 6x - 6x)y(x) +--R +--R Type: Expression Integer +--E 86 + +--S 87 of 130 +yx:=solve(ode283,y,x) +--R +--R +--R x 3 3 2 x 2 +--R (86) - (%e ) + (y(x) - 3x y(x))(%e ) +--R Type: Union(Expression Integer,...) +--E 87 + +--S 88 of 130 +ode283expr := 3*(yx**2-x**2)*D(yx,x)+2*yx**3-6*x*(x+1)*yx-3*exp(x) +--R +--R +--R (87) +--R 2 2 x 8 5 2 3 4 x 7 +--R (9y(x) - 9x )(%e ) + (- 18y(x) + 72x y(x) - 54x y(x))(%e ) +--R + +--R 8 2 6 4 4 6 2 x 6 +--R (9y(x) - 63x y(x) + 135x y(x) - 81x y(x) )(%e ) +--R + +--R 2 2 4 x 2 +--R (- 9x y(x) + 9x )(%e ) +--R * +--R , +--R y (x) +--R +--R + +--R x 9 3 2 x 8 +--R - 11(%e ) + (30y(x) + (- 90x - 18x)y(x))(%e ) +--R + +--R 6 2 4 4 3 2 x 7 +--R (- 27y(x) + (162x + 36x)y(x) + (- 243x - 108x )y(x) )(%e ) +--R + +--R 9 2 7 4 3 5 +--R 8y(x) + (- 72x - 18x)y(x) + (216x + 108x )y(x) +--R + +--R 6 5 3 +--R (- 216x - 162x )y(x) +--R * +--R x 6 +--R (%e ) +--R + +--R 2 x 3 2 3 4 3 x 2 x +--R (15x + 6x)(%e ) + ((- 12x - 6x)y(x) + (36x + 36x )y(x))(%e ) - 3%e +--R Type: Expression Integer +--E 88 + +--S 89 of 130 +ode284 := (4*y(x)**2+x**2)*D(y(x),x)-x*y(x) +--R +--R +--R 2 2 , +--R (88) (4y(x) + x )y (x) - x y(x) +--R +--R Type: Expression Integer +--E 89 + +--S 90 of 130 +yx:=solve(ode284,y,x) +--R +--R +--R 2 2 +--R 8y(x) log(y(x)) - x +--R (89) -------------------- +--R 2 +--R 2y(x) +--R Type: Union(Expression Integer,...) +--E 90 + +--S 91 of 130 +ode284expr := (4*yx**2+x**2)*D(yx,x)-x*yx +--R +--R +--R (90) +--R 6 2 4 2 +--R (512y(x) + 128x y(x) )log(y(x)) +--R + +--R 2 4 4 2 2 6 4 4 4 2 +--R (- 128x y(x) - 32x y(x) )log(y(x)) + 8x y(x) + 2x y(x) + 8x y(x) +--R + +--R 6 +--R 2x +--R * +--R , +--R y (x) +--R +--R + +--R 5 2 7 3 3 3 5 +--R - 128x y(x) log(y(x)) + (- 8x y(x) + 32x y(x) )log(y(x)) - x y(x) +--R + +--R 5 +--R - 2x y(x) +--R / +--R 7 +--R 2y(x) +--R Type: Expression Integer +--E 91 + +--S 92 of 130 +ode285 := (4*y(x)**2+2*x*y(x)+3*x**2)*D(y(x),x)+y(x)**2+6*x*y(x)+2*x**2 +--R +--R +--R 2 2 , 2 2 +--R (91) (4y(x) + 2x y(x) + 3x )y (x) + y(x) + 6x y(x) + 2x +--R +--R Type: Expression Integer +--E 92 + +--S 93 of 130 +yx:=solve(ode285,y,x) +--R +--R +--R 3 2 2 3 +--R 4y(x) + 3x y(x) + 9x y(x) + 2x +--R (92) --------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 93 + +--S 94 of 130 +ode285expr := (4*yx**2+2*x*yx+3*x**2)*D(yx,x)+yx**2+6*x*yx+2*x**2 +--R +--R +--R (93) +--R 8 7 2 6 3 5 +--R 256y(x) + 512x y(x) + 1680x y(x) + (2056x + 96x)y(x) +--R + +--R 4 2 4 5 3 3 +--R (3020x + 120x )y(x) + (2160x + 324x )y(x) +--R + +--R 6 4 2 2 7 5 3 8 +--R (1468x + 210x + 108x )y(x) + (464x + 186x + 54x )y(x) + 48x +--R + +--R 6 4 +--R 36x + 81x +--R * +--R , +--R y (x) +--R +--R + +--R 8 7 2 6 3 5 +--R 64y(x) + 480x y(x) + (1028x + 16)y(x) + (2416x + 48x)y(x) +--R + +--R 4 2 4 5 3 3 +--R (2700x + 243x )y(x) + (2936x + 280x + 72x)y(x) +--R + +--R 6 4 2 2 7 5 3 8 6 +--R (1624x + 465x + 81x )y(x) + (384x + 216x + 324x )y(x) + 32x + 28x +--R + +--R 4 2 +--R 90x + 18x +--R / +--R 9 +--R Type: Expression Integer +--E 94 + +--S 95 of 130 +ode286 := (2*y(x)-3*x+1)**2*D(y(x),x)-(3*y(x)-2*x-4)**2 +--R +--R +--R (94) +--R 2 2 , 2 +--R (4y(x) + (- 12x + 4)y(x) + 9x - 6x + 1)y (x) - 9y(x) + (12x + 24)y(x) +--R +--R + +--R 2 +--R - 4x - 16x - 16 +--R Type: Expression Integer +--E 95 + +--S 96 of 130 +solve(ode286,y,x) +--R +--R +--R (95) "failed" +--R Type: Union("failed",...) +--E 96 + +--S 97 of 130 +ode287 := (2*y(x)-4*x+1)**2*D(y(x),x)-(y(x)-2*x)**2 +--R +--R +--R (96) +--R 2 2 , 2 2 +--R (4y(x) + (- 16x + 4)y(x) + 16x - 8x + 1)y (x) - y(x) + 4x y(x) - 4x +--R +--R Type: Expression Integer +--E 97 + +--S 98 of 130 +solve(ode287,y,x) +--R +--R +--R (97) "failed" +--R Type: Union("failed",...) +--E 98 + +--S 99 of 130 +ode288 := (6*y(x)**2-3*x**2*y(x)+1)*D(y(x),x)-3*x*y(x)**2+x +--R +--R +--R 2 2 , 2 +--R (98) (6y(x) - 3x y(x) + 1)y (x) - 3x y(x) + x +--R +--R Type: Expression Integer +--E 99 + +--S 100 of 130 +yx:=solve(ode288,y,x) +--R +--R +--R 3 2 2 2 +--R 4y(x) - 3x y(x) + 2y(x) + x +--R (99) ------------------------------ +--R 2 +--R Type: Union(Expression Integer,...) +--E 100 + +--S 101 of 130 +ode288expr := (6*yx**2-3*x**2*yx+1)*D(yx,x)-3*x*yx**2+x +--R +--R +--R (100) +--R 8 2 7 4 6 6 2 5 +--R 576y(x) - 1152x y(x) + (756x + 672)y(x) + (- 162x - 720x )y(x) +--R + +--R 4 4 6 2 3 4 2 +--R (90x + 240)y(x) + (54x - 48x )y(x) + (- 54x + 48)y(x) + 4 +--R * +--R , +--R y (x) +--R +--R + +--R 8 3 7 5 6 3 5 +--R - 288x y(x) + 432x y(x) + (- 162x - 240x)y(x) + 72x y(x) +--R + +--R 5 4 3 3 5 +--R (81x - 24x)y(x) - 72x y(x) - 3x + 8x +--R / +--R 4 +--R Type: Expression Integer +--E 101 + +--S 102 of 130 +ode289 := (6*y(x)-x)**2*D(y(x),x)-6*y(x)**2+2*x*y(x)+a +--R +--R +--R 2 2 , 2 +--R (101) (36y(x) - 12x y(x) + x )y (x) - 6y(x) + 2x y(x) + a +--R +--R Type: Expression Integer +--E 102 + +--S 103 of 130 +yx:=solve(ode289,y,x) +--R +--R +--R 3 2 2 +--R (102) 12y(x) - 6x y(x) + x y(x) + a x +--R Type: Union(Expression Integer,...) +--E 103 + +--S 104 of 130 +ode289expr := (6*yx-x)**2*D(yx,x)-6*yx**2+2*x*yx+a +--R +--R +--R (103) +--R 8 7 2 6 +--R 186624y(x) - 248832x y(x) + 145152x y(x) +--R + +--R 3 5 +--R (- 46656x + (31104a - 5184)x)y(x) +--R + +--R 4 2 4 5 3 3 +--R (8640x + (- 25920a + 4320)x )y(x) + (- 864x + (8640a - 1440)x )y(x) +--R + +--R 6 4 2 2 2 +--R (36x + (- 1296a + 216)x + (1296a - 432a + 36)x )y(x) +--R + +--R 5 2 3 2 4 +--R ((72a - 12)x + (- 432a + 144a - 12)x )y(x) + (36a - 12a + 1)x +--R * +--R , +--R y (x) +--R +--R + +--R 8 7 2 6 +--R - 31104y(x) + 41472x y(x) + (- 23328x + 5184a - 864)y(x) +--R + +--R 3 5 4 2 4 +--R (6912x + (- 10368a + 1728)x)y(x) + (- 1080x + (6480a - 1080)x )y(x) +--R + +--R 5 3 2 3 +--R (72x + (- 1728a + 288)x + (864a - 288a + 24)x)y(x) +--R + +--R 4 2 2 2 2 3 +--R ((180a - 30)x + (- 648a + 216a - 18)x )y(x) + (144a - 48a + 4)x y(x) +--R + +--R 3 2 2 +--R (36a - 18a + 3a)x + a +--R Type: Expression Integer +--E 104 + +--S 105 of 130 +ode290 := (a*y(x)**2+2*b*x*y(x)+c*x**2)*D(y(x),x)+b*y(x)**2+2*c*x*y(x)+d*x**2 +--R +--R +--R 2 2 , 2 2 +--R (104) (a y(x) + 2b x y(x) + c x )y (x) + b y(x) + 2c x y(x) + d x +--R +--R Type: Expression Integer +--E 105 + +--S 106 of 130 +yx:=solve(ode290,y,x) +--R +--R +--R 3 2 2 3 +--R a y(x) + 3b x y(x) + 3c x y(x) + d x +--R (105) --------------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 106 + +--S 107 of 130 +ode290expr:=(a*yx**2+2*b*x*yx+c*x**2)*D(yx,x)+b*yx**2+2*c*x*yx+d*x**2 +--R +--R +--R (106) +--R 4 8 3 7 3 2 2 2 6 +--R a y(x) + 8a b x y(x) + (7a c + 21a b )x y(x) +--R + +--R 3 2 3 3 2 5 +--R ((2a d + 36a b c + 18a b )x + 6a b x)y(x) +--R + +--R 2 2 2 2 4 2 2 4 +--R ((10a b d + 15a c + 45a b c)x + 30a b x )y(x) +--R + +--R 2 2 2 5 3 3 3 +--R (((8a c + 12a b )d + 36a b c )x + (24a b c + 36b )x )y(x) +--R + +--R 2 2 3 6 2 4 2 2 +--R ((a d + 18a b c d + 9a c )x + (6a b d + 54b c)x + 9a c x )y(x) +--R + +--R 2 2 7 2 2 5 3 2 8 +--R ((2a b d + 6a c d)x + (12b d + 18b c )x + 18b c x )y(x) + a c d x +--R + +--R 6 2 4 +--R 6b c d x + 9c x +--R * +--R , +--R y (x) +--R +--R + +--R 3 8 3 2 2 7 +--R a b y(x) + (2a c + 6a b )x y(x) +--R + +--R 3 2 3 2 2 6 +--R ((a d + 18a b c + 9a b )x + a b)y(x) +--R + +--R 2 2 2 2 3 2 5 +--R ((8a b d + 12a c + 36a b c)x + 12a b x)y(x) +--R + +--R 2 2 2 4 3 2 4 +--R (((10a c + 15a b )d + 45a b c )x + (18a b c + 27b )x )y(x) +--R + +--R 2 2 3 5 2 3 3 +--R ((2a d + 36a b c d + 18a c )x + (8a b d + 72b c)x + 6a c x)y(x) +--R + +--R 2 2 6 2 2 4 2 2 +--R ((7a b d + 21a c d)x + (30b d + 45b c )x + 27b c x )y(x) +--R + +--R 2 7 5 2 3 3 8 2 6 4 2 +--R (8a c d x + 36b c d x + 36c x )y(x) + a d x + 7b d x + 15c d x + 9d x +--R / +--R 9 +--R Type: Expression Integer +--E 107 + +--S 108 of 130 +ode291 := (b*(beta*y(x)+alpha*x)**2-beta*(b*y(x)+a*x))*D(y(x),x)+_ + a*(beta*y(x)+alpha*x)**2-alpha*(b*y(x)+a*x) +--R +--R +--R (107) +--R 2 2 2 2 +--R (b beta y(x) + (2alpha b beta x - b beta)y(x) + alpha b x - a beta x) +--R * +--R , +--R y (x) +--R +--R + +--R 2 2 2 2 +--R a beta y(x) + (2a alpha beta x - alpha b)y(x) + a alpha x - a alpha x +--R Type: Expression Integer +--E 108 + +--S 109 of 130 +solve(ode291,y,x) +--R +--R +--R (108) "failed" +--R Type: Union("failed",...) +--E 109 + +--S 110 of 130 +ode292 := (a*y(x)+b*x+c)**2*D(y(x),x)+(alpha*y(x)+beta*x+gamma)**2 +--R +--R +--R (109) +--R 2 2 2 2 2 , 2 2 +--R (a y(x) + (2a b x + 2a c)y(x) + b x + 2b c x + c )y (x) + alpha y(x) +--R +--R + +--R 2 2 2 +--R (2alpha beta x + 2alpha gamma)y(x) + beta x + 2beta gamma x + gamma +--R Type: Expression Integer +--E 110 + +--S 111 of 130 +solve(ode292,y,x) +--R +--R +--R (110) "failed" +--R Type: Union("failed",...) +--E 111 + +--S 112 of 130 +ode293 := x*(y(x)**2-3*x)*D(y(x),x)+2*y(x)**3-5*x*y(x) +--R +--R +--R 2 2 , 3 +--R (111) (x y(x) - 3x )y (x) + 2y(x) - 5x y(x) +--R +--R Type: Expression Integer +--E 112 + +--S 113 of 130 +solve(ode293,y,x) +--R +--R +--R (112) "failed" +--R Type: Union("failed",...) +--E 113 + +--S 114 of 130 +ode294 := x*(y(x)**2+x**2-a)*D(y(x),x)-y(x)*(y(x)**2+x**2+a) +--R +--R +--R 2 3 , 3 2 +--R (113) (x y(x) + x - a x)y (x) - y(x) + (- x - a)y(x) +--R +--R Type: Expression Integer +--E 114 + +--S 115 of 130 +solve(ode294,y,x) +--R +--R +--R (114) "failed" +--R Type: Union("failed",...) +--E 115 + +--S 116 of 130 +ode295 := x*(y(x)**2+x*y(x)-x**2)*D(y(x),x)-y(x)**3+x*y(x)**2+x**2*y(x) +--R +--R +--R 2 2 3 , 3 2 2 +--R (115) (x y(x) + x y(x) - x )y (x) - y(x) + x y(x) + x y(x) +--R +--R Type: Expression Integer +--E 116 + +--S 117 of 130 +solve(ode295,y,x) +--R +--R +--R (116) "failed" +--R Type: Union("failed",...) +--E 117 + +--S 118 of 130 +ode296 := x*(y(x)**2+x**2*y(x)+x**2)*D(y(x),x)-2*y(x)**3-2*x**2*y(x)**2+x**4 +--R +--R +--R 2 3 3 , 3 2 2 4 +--R (117) (x y(x) + x y(x) + x )y (x) - 2y(x) - 2x y(x) + x +--R +--R Type: Expression Integer +--E 118 + +--S 119 of 130 +solve(ode296,y,x) +--R +--R +--R (118) "failed" +--R Type: Union("failed",...) +--E 119 + +--S 120 of 130 +ode297 := 2*x*(y(x)**2+5*x**2)*D(y(x),x)+y(x)**3-x**2*y(x) +--R +--R +--R 2 3 , 3 2 +--R (119) (2x y(x) + 10x )y (x) + y(x) - x y(x) +--R +--R Type: Expression Integer +--E 120 + +--S 121 of 130 +solve(ode297,y,x) +--R +--R +--R (120) "failed" +--R Type: Union("failed",...) +--E 121 + +--S 122 of 130 +ode298 := 3*x*y(x)**2*D(y(x),x)+y(x)**3-2*x +--R +--R +--R 2 , 3 +--R (121) 3x y(x) y (x) + y(x) - 2x +--R +--R Type: Expression Integer +--E 122 + +--S 123 of 130 +yx:=solve(ode298,y,x) +--R +--R +--R 3 2 +--R (122) x y(x) - x +--R Type: Union(Expression Integer,...) +--E 123 + +--S 124 of 130 +ode298expr := 3*x*yx**2*D(yx,x)+yx**3-2*x +--R +--R +--R (123) +--R 4 8 5 5 6 2 , 3 9 4 6 5 3 +--R (9x y(x) - 18x y(x) + 9x y(x) )y (x) + 4x y(x) - 15x y(x) + 18x y(x) +--R +--R + +--R 6 +--R - 7x - 2x +--R Type: Expression Integer +--E 124 + +--S 125 of 130 +ode299 := (3*x*y(x)**2-x**2)*D(y(x),x)+y(x)**3-2*x*y(x) +--R +--R +--R 2 2 , 3 +--R (124) (3x y(x) - x )y (x) + y(x) - 2x y(x) +--R +--R Type: Expression Integer +--E 125 + +--S 126 of 130 +yx:=solve(ode299,y,x) +--R +--R +--R 3 2 +--R (125) x y(x) - x y(x) +--R Type: Union(Expression Integer,...) +--E 126 + +--S 127 of 130 +ode299expr := (3*x*yx**2-x**2)*D(yx,x)+yx**3-2*x*yx +--R +--R +--R (126) +--R 4 8 5 6 6 4 7 3 2 4 , +--R (9x y(x) - 21x y(x) + 15x y(x) + (- 3x - 3x )y(x) + x )y (x) +--R +--R + +--R 3 9 4 7 5 5 6 2 3 3 +--R 4x y(x) - 15x y(x) + 18x y(x) + (- 7x - 3x )y(x) + 4x y(x) +--R Type: Expression Integer +--E 127 + +--S 128 of 130 +ode300 := 6*x*y(x)**2*D(y(x),x)+2*y(x)**3+x +--R +--R +--R 2 , 3 +--R (127) 6x y(x) y (x) + 2y(x) + x +--R +--R Type: Expression Integer +--E 128 + +--S 129 of 130 +yx:=solve(ode300,y,x) +--R +--R +--R 3 2 +--R 4x y(x) + x +--R (128) ------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 129 + +--S 130 of 130 +ode300expr := 6*x*yx**2*D(yx,x)+2*yx**3+x +--R +--R +--R (129) +--R 4 8 5 5 6 2 , 3 9 4 6 +--R (576x y(x) + 288x y(x) + 36x y(x) )y (x) + 256x y(x) + 240x y(x) +--R +--R + +--R 5 3 6 +--R 72x y(x) + 7x + 4x +--R / +--R 4 +--R Type: Expression Integer +--E 130 + +)spool +)lisp (bye) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} {\bf http://www.cs.uwaterloo.ca/$\tilde{}$ecterrab/odetools.html} +\end{thebibliography} +\end{document}