diff --git a/changelog b/changelog index c63be68..7c61a45 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,5 @@ +20071005 tpd src/input/Makefile kamke7.input regression test added +20071005 tpd src/input/kamke7.input ODE regression test added 20071005 tpd src/input/Makefile kamke6.input regression test added 20071005 tpd src/input/kamke6.input ODE regression test added 20071005 tpd src/input/Makefile kamke5.input regression test added diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 3d92581..f1f937b 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 kamke5.regress kamke6.regress \ + kamke4.regress kamke5.regress kamke6.regress kamke7.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 \ @@ -564,7 +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}/kamke6.input \ + ${OUT}/kamke5.input ${OUT}/kamke6.input ${OUT}/kamke7.input \ ${OUT}/kernel.input ${OUT}/knot.input \ ${OUT}/kovacic.input ${OUT}/kuipers.input \ ${OUT}/laplace.input ${OUT}/leg.input ${OUT}/lexp.input \ @@ -833,7 +833,7 @@ DOCFILES= \ ${DOC}/kamke0.input.dvi ${DOC}/kamke1.input.dvi \ ${DOC}/kamke2.input.dvi ${DOC}/kamke3.input.dvi \ ${DOC}/kamke4.input.dvi ${DOC}/kamke5.input.dvi \ - ${DOC}/kamke6.input.dvi \ + ${DOC}/kamke6.input.dvi ${DOC}/kamke7.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/kamke7.input.pamphlet b/src/input/kamke7.input.pamphlet new file mode 100644 index 0000000..eb989d3 --- /dev/null +++ b/src/input/kamke7.input.pamphlet @@ -0,0 +1,1538 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input kamke7.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This is the remaining 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. + +Note that after a certain point Axiom can no longer generate useful +results. The failures fall into several cases which have been included +in other regression test files. +\end{abstract} +\eject +\tableofcontents +\eject +\section{Generated results} +<<*>>= +)spool kamke7.output +)set break resume +)set mes auto off +)clear all + +--S 1 of 97 +y:=operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 1 + +--S 2 of 97 +f:=operator 'f +--R +--R +--R (2) f +--R Type: BasicOperator +--E 2 + +--S 3 of 97 +g:=operator 'g +--R +--R +--R (3) g +--R Type: BasicOperator +--E 3 + +--S 4 of 97 +h:=operator 'h +--R +--R +--R (4) h +--R Type: BasicOperator +--E 4 + +--S 5 of 97 +fa:=operator 'fa +--R +--R +--R (5) fa +--R Type: BasicOperator +--E 5 + +--S 6 of 97 +fb:=operator 'fb +--R +--R +--R (6) fb +--R Type: BasicOperator +--E 6 + +--S 7 of 97 +fc:=operator 'fc +--R +--R +--R (7) fc +--R Type: BasicOperator +--E 7 + +--S 8 of 97 +fd:=operator 'fd +--R +--R +--R (8) fd +--R Type: BasicOperator +--E 8 + +--S 9 of 97 +fe:=operator 'fe +--R +--R +--R (9) fe +--R Type: BasicOperator +--E 9 + +--S 10 of 97 +ff:=operator 'ff +--R +--R +--R (10) ff +--R Type: BasicOperator +--E 10 + +--S 11 of 97 +ode352 := D(y(x),x)*(cos(y(x))-sin(alpha)*sin(x))*cos(y(x))+(cos(x)-_ + sin(alpha)*sin(y(x)))*cos(x) +--R +--R +--R (11) +--R 2 , +--R (cos(y(x)) - sin(alpha)sin(x)cos(y(x)))y (x) - cos(x)sin(alpha)sin(y(x)) +--R +--R + +--R 2 +--R cos(x) +--R Type: Expression Integer +--E 11 + +--S 12 of 97 +yx:=solve(ode352,y,x) +--R +--R +--R (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x +--R (12) ------------------------------------------------------------------ +--R 2 +--R Type: Union(Expression Integer,...) +--E 12 + +--S 13 of 97 +ode352expr := D(yx,x)*(cos(yx)-sin(alpha)*sin(x))*cos(yx)+(cos(x)-_ + sin(alpha)*sin(yx))*cos(x) +--R +--R +--R (13) +--R - +--R 2cos(x)sin(alpha) +--R * +--R sin +--R (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) +--R + +--R y(x) + x +--R / +--R 2 +--R + +--R 2 2 , +--R (- sin(y(x)) + cos(y(x)) - 2sin(alpha)sin(x)cos(y(x)) + 1)y (x) +--R +--R + +--R 2 2 +--R - 2cos(x)sin(alpha)sin(y(x)) - sin(x) + cos(x) + 1 +--R * +--R (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x 2 +--R cos(------------------------------------------------------------------) +--R 2 +--R + +--R 2 2 +--R sin(alpha)sin(x)sin(y(x)) - sin(alpha)sin(x)cos(y(x)) +--R + +--R 2 2 +--R 2sin(alpha) sin(x) cos(y(x)) - sin(alpha)sin(x) +--R * +--R , +--R y (x) +--R +--R + +--R 2 3 +--R 2cos(x)sin(alpha) sin(x)sin(y(x)) + sin(alpha)sin(x) +--R + +--R 2 +--R (- cos(x) - 1)sin(alpha)sin(x) +--R * +--R (cos(y(x)) - 2sin(alpha)sin(x))sin(y(x)) + cos(x)sin(x) + y(x) + x +--R cos(------------------------------------------------------------------) +--R 2 +--R + +--R 2 +--R 2cos(x) +--R / +--R 2 +--R Type: Expression Integer +--E 13 + +--S 14 of 97 +ode353 := x*D(y(x),x)*cos(y(x))+sin(y(x)) +--R +--R +--R , +--R (14) x cos(y(x))y (x) + sin(y(x)) +--R +--R Type: Expression Integer +--E 14 + +--S 15 of 97 +yx:=solve(ode353,y,x) +--R +--R +--R (15) x sin(y(x)) +--R Type: Union(Expression Integer,...) +--E 15 + +--S 16 of 97 +ode353expr := x*D(yx,x)*cos(yx)+sin(yx) +--R +--R +--R 2 , +--R (16) sin(x sin(y(x))) + (x cos(y(x))y (x) + x sin(y(x)))cos(x sin(y(x))) +--R +--R Type: Expression Integer +--E 16 + +--S 17 of 97 +ode354 := (x*sin(y(x))-1)*D(y(x),x)+cos(y(x)) +--R +--R +--R , +--R (17) (x sin(y(x)) - 1)y (x) + cos(y(x)) +--R +--R Type: Expression Integer +--E 17 + +--S 18 of 97 +yx:=solve(ode354,y,x) +--R +--R +--R - sin(y(x)) + x +--R (18) --------------- +--R cos(y(x)) +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 97 +ode354expr := (x*sin(yx)-1)*D(yx,x)+cos(yx) +--R +--R +--R (19) +--R 2 2 2 , +--R ((x sin(y(x)) - x sin(y(x)) + x cos(y(x)) )y (x) - x cos(y(x))) +--R +--R * +--R sin(y(x)) - x +--R sin(-------------) +--R cos(y(x)) +--R + +--R 2 sin(y(x)) - x +--R cos(y(x)) cos(-------------) +--R cos(y(x)) +--R + +--R 2 2 , +--R (sin(y(x)) - x sin(y(x)) + cos(y(x)) )y (x) - cos(y(x)) +--R +--R / +--R 2 +--R cos(y(x)) +--R Type: Expression Integer +--E 19 + +--S 20 of 97 +ode355 := (x*cos(y(x))+cos(x))*D(y(x),x)-y(x)*sin(x)+sin(y(x)) +--R +--R +--R , +--R (20) (x cos(y(x)) + cos(x))y (x) + sin(y(x)) - y(x)sin(x) +--R +--R Type: Expression Integer +--E 20 + +--S 21 of 97 +yx:=solve(ode355,y,x) +--R +--R +--R (21) x sin(y(x)) + y(x)cos(x) +--R Type: Union(Expression Integer,...) +--E 21 + +--S 22 of 97 +ode355expr := (x*cos(yx)+cos(x))*D(yx,x)-yx*sin(x)+sin(yx) +--R +--R +--R (22) +--R sin(x sin(y(x)) + y(x)cos(x)) +--R + +--R 2 , +--R ((x cos(y(x)) + x cos(x))y (x) + x sin(y(x)) - x y(x)sin(x)) +--R +--R * +--R cos(x sin(y(x)) + y(x)cos(x)) +--R + +--R 2 , +--R (x cos(x)cos(y(x)) + cos(x) )y (x) + (- x sin(x) + cos(x))sin(y(x)) +--R +--R + +--R - 2y(x)cos(x)sin(x) +--R Type: Expression Integer +--E 22 + +--S 23 of 97 +ode356 := (x**2*cos(y(x))+2*y(x)*sin(x))*D(y(x),x)+2*x*sin(y(x))+y(x)**2*cos(x) +--R +--R +--R 2 , 2 +--R (23) (x cos(y(x)) + 2y(x)sin(x))y (x) + 2x sin(y(x)) + y(x) cos(x) +--R +--R Type: Expression Integer +--E 23 + +--S 24 of 97 +yx:=solve(ode356,y,x) +--R +--R +--R 2 2 +--R (24) x sin(y(x)) + y(x) sin(x) +--R Type: Union(Expression Integer,...) +--E 24 + +--S 25 of 97 +ode356expr:=(x**2*cos(yx)+2*yx*sin(x))*D(yx,x)+2*x*sin(yx)+yx**2*cos(x) +--R +--R +--R (25) +--R 2 2 +--R 2x sin(x sin(y(x)) + y(x) sin(x)) +--R + +--R 4 2 , 3 2 2 +--R ((x cos(y(x)) + 2x y(x)sin(x))y (x) + 2x sin(y(x)) + x y(x) cos(x)) +--R +--R * +--R 2 2 +--R cos(x sin(y(x)) + y(x) sin(x)) +--R + +--R 4 2 2 +--R (2x sin(x)cos(y(x)) + 4x y(x)sin(x) )sin(y(x)) +--R + +--R 2 2 2 3 3 +--R 2x y(x) sin(x) cos(y(x)) + 4y(x) sin(x) +--R * +--R , +--R y (x) +--R +--R + +--R 3 4 2 +--R (4x sin(x) + x cos(x))sin(y(x)) +--R + +--R 2 2 2 2 4 2 +--R (4x y(x) sin(x) + 4x y(x) cos(x)sin(x))sin(y(x)) + 3y(x) cos(x)sin(x) +--R Type: Expression Integer +--E 25 + +--S 26 of 97 +ode358 := D(y(x),x)*sin(y(x))*cos(x)+cos(y(x))*sin(x) +--R +--R +--R , +--R (26) cos(x)sin(y(x))y (x) + sin(x)cos(y(x)) +--R +--R Type: Expression Integer +--E 26 + +--S 27 of 97 +yx:=solve(ode358,y,x) +--R +--R +--R (27) - cos(x)cos(y(x)) +--R Type: Union(Expression Integer,...) +--E 27 + +--S 28 of 97 +ode358expr := D(yx,x)*sin(yx)*cos(x)+cos(yx)*sin(x) +--R +--R +--R (28) +--R 2 , +--R (- cos(x) sin(y(x))y (x) - cos(x)sin(x)cos(y(x)))sin(cos(x)cos(y(x))) +--R +--R + +--R sin(x)cos(cos(x)cos(y(x))) +--R Type: Expression Integer +--E 28 + +--S 29 of 97 +ode361 := (x*sin(x*y(x))+cos(x+y(x))-sin(y(x)))*D(y(x),x)+_ + y(x)*sin(x*y(x))+cos(x+y(x))+cos(x) +--R +--R +--R (29) +--R , +--R (x sin(x y(x)) - sin(y(x)) + cos(y(x) + x))y (x) + y(x)sin(x y(x)) +--R +--R + +--R cos(y(x) + x) + cos(x) +--R Type: Expression Integer +--E 29 + +--S 30 of 97 +yx:=solve(ode361,y,x) +--R +--R +--R (30) +--R y(x) 2 y(x) y(x) +--R 2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----) - cos(x y(x)) +--R 2 2 2 +--R + +--R cos(y(x)) +--R Type: Union(Expression Integer,...) +--E 30 + +--S 31 of 97 +ode361expr:=(x*sin(x*yx)+cos(x+yx)-sin(yx))*D(yx,x)+_ + yx*sin(x*yx)+cos(x+yx)+cos(x) +--R +--R +--R (31) +--R 2 y(x) 2 +--R x sin(x y(x)) - x sin(y(x)) + x cos(y(x) + x)sin(----) +--R 2 +--R + +--R y(x) 2 +--R x cos(----) cos(y(x) + x) +--R 2 +--R * +--R , +--R y (x) +--R +--R + +--R y(x) y(x) y(x) 2 +--R x y(x)sin(x y(x)) + (2x cos(----)sin(----) + 2cos(----) )sin(y(x) + x) +--R 2 2 2 +--R + +--R y(x) y(x) +--R - 2cos(----)cos(y(x) + x)sin(----) - cos(x y(x)) +--R 2 2 +--R + +--R y(x) 2 +--R 2x cos(----) cos(y(x) + x) + cos(y(x)) +--R 2 +--R * +--R sin +--R y(x) 2 y(x) y(x) +--R 2x cos(----) sin(y(x) + x) - 2x cos(----)cos(y(x) + x)sin(----) +--R 2 2 2 +--R + +--R - x cos(x y(x)) + x cos(y(x)) +--R + +--R y(x) 2 +--R - x sin(x y(x)) + sin(y(x)) - cos(y(x) + x)sin(----) +--R 2 +--R + +--R y(x) 2 +--R - cos(----) cos(y(x) + x) +--R 2 +--R * +--R , +--R y (x) +--R +--R + +--R y(x) y(x) +--R - y(x)sin(x y(x)) - 2cos(----)sin(----)sin(y(x) + x) +--R 2 2 +--R + +--R y(x) 2 +--R - 2cos(----) cos(y(x) + x) +--R 2 +--R * +--R sin +--R y(x) 2 y(x) y(x) +--R 2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----) +--R 2 2 2 +--R + +--R - cos(x y(x)) + cos(y(x)) +--R + +--R y(x) 2 +--R x sin(x y(x)) - sin(y(x)) + cos(y(x) + x)sin(----) +--R 2 +--R + +--R y(x) 2 +--R cos(----) cos(y(x) + x) +--R 2 +--R * +--R , +--R y (x) +--R +--R + +--R y(x) y(x) +--R y(x)sin(x y(x)) + 2cos(----)sin(----)sin(y(x) + x) +--R 2 2 +--R + +--R y(x) 2 +--R 2cos(----) cos(y(x) + x) + 1 +--R 2 +--R * +--R cos +--R y(x) 2 y(x) y(x) +--R 2cos(----) sin(y(x) + x) - 2cos(----)cos(y(x) + x)sin(----) +--R 2 2 2 +--R + +--R - cos(x y(x)) + cos(y(x)) + x +--R + +--R cos(x) +--R Type: Expression Integer +--E 31 + +--S 32 of 97 +ode363 := (x*D(y(x),x)-y(x))*cos(y(x)/x)**2+x +--R +--R +--R y(x) 2 , y(x) 2 +--R (32) x cos(----) y (x) - y(x)cos(----) + x +--R x x +--R Type: Expression Integer +--E 32 + +--S 33 of 97 +yx:=solve(ode363,y,x) +--R +--R +--R y(x) y(x) +--R x cos(----)sin(----) + 2x log(x) + y(x) +--R x x +--R (33) --------------------------------------- +--R 2x +--R Type: Union(Expression Integer,...) +--E 33 + +--S 34 of 97 +ode363expr := (x*D(yx,x)-yx)*cos(yx/x)**2+x +--R +--R +--R (34) +--R y(x) 2 y(x) 2 , y(x) 2 +--R (- x sin(----) + x cos(----) + x)y (x) + y(x)sin(----) +--R x x x +--R + +--R y(x) y(x) y(x) 2 +--R - x cos(----)sin(----) - y(x)cos(----) - 2x log(x) - 2y(x) + 2x +--R x x x +--R * +--R y(x) y(x) 2 +--R x cos(----)sin(----) + 2x log(x) + y(x) +--R x x +--R cos(---------------------------------------) +--R 2 +--R 2x +--R + +--R 2 +--R 2x +--R / +--R 2x +--R Type: Expression Integer +--E 34 + +--S 35 of 97 +ode364 := (y(x)*sin(y(x)/x)-x*cos(y(x)/x))*x*D(y(x),x)-_ + (x*cos(y(x)/x)+y(x)*sin(y(x)/x))*y(x) +--R +--R +--R (35) +--R y(x) 2 y(x) , 2 y(x) y(x) +--R (x y(x)sin(----) - x cos(----))y (x) - y(x) sin(----) - x y(x)cos(----) +--R x x x x +--R Type: Expression Integer +--E 35 + +--S 36 of 97 +yx:=solve(ode364,y,x) +--R +--R +--R y(x) +--R (36) - x y(x)cos(----) +--R x +--R Type: Union(Expression Integer,...) +--E 36 + +--S 37 of 97 +ode364expr := (yx*sin(yx/x)-x*cos(yx/x))*x*D(yx,x)-_ + (x*cos(yx/x)+yx*sin(yx/x))*yx +--R +--R +--R (37) +--R 2 2 y(x) y(x) 3 y(x) 2 , +--R (x y(x) cos(----)sin(----) - x y(x)cos(----) )y (x) +--R x x x +--R + +--R 3 y(x) y(x) +--R - x y(x) cos(----)sin(----) +--R x x +--R * +--R y(x) +--R sin(y(x)cos(----)) +--R x +--R + +--R 2 y(x) 3 y(x) , 2 y(x) +--R (- x y(x)sin(----) + x cos(----))y (x) + x y(x) sin(----) +--R x x x +--R + +--R 2 y(x) +--R 2x y(x)cos(----) +--R x +--R * +--R y(x) +--R cos(y(x)cos(----)) +--R x +--R Type: Expression Integer +--E 37 + +--S 38 of 97 +ode434 := D(y(x),x)-1 +--R +--R +--R , +--R (38) y (x) - 1 +--R +--R Type: Expression Integer +--E 38 + +--S 39 of 97 +ode434a:=solve(ode434,y,x) +--R +--R +--R (39) [particular= x,basis= [1]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 39 + +--S 40 of 97 +yx:=ode434a.particular +--R +--R +--R (40) x +--R Type: Expression Integer +--E 40 + +--S 41 of 97 +ode434expr := D(yx,x)-1 +--R +--R +--R (41) 0 +--R Type: Expression Integer +--E 41 + +--S 42 of 97 +ode683 := (D(y(x),x) = y(x)*(-1+log(x*(x+1))*y(x)*x**4-log(x*(x+1))*x**3)/x) +--R +--R +--R 4 2 3 2 +--R , (x y(x) - x y(x))log(x + x) - y(x) +--R (42) y (x)= ------------------------------------ +--R x +--R Type: Equation Expression Integer +--E 42 + +--S 43 of 97 +solve(ode683,y,x) +--R +--R +--R - x y(x) + 1 +--R (43) ----------------------------------------------- +--R 3 2 3 2 +--R 6x log(x + x) - 4x + 3x - 6x +--R ------------------------------- +--R 3+-----+ 18 +--R x y(x)\|x + 1 %e +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 97 +ode703 := (D(y(x),x) = y(x)*(1-x+y(x)*x**2*log(x)+y(x)*x**3-x*log(x)-x**2)/_ + (x-1)/x) +--R +--R +--R 2 2 3 2 2 +--R , (x y(x) - x y(x))log(x) + x y(x) + (- x - x + 1)y(x) +--R (44) y (x)= ------------------------------------------------------- +--R 2 +--R x - x +--R Type: Equation Expression Integer +--E 44 + +--S 45 of 97 +solve(ode703,y,x) +--R +--R +--R - x y(x) + 1 +--R (45) ---------------------------- +--R 2 - dilog(x) + x +--R (x - x)y(x)%e +--R Type: Union(Expression Integer,...) +--E 45 + +--S 46 of 97 +ode714 := (D(y(x),x) = -y(x)*(-log(1/x)+exp(x)+y(x)*x**2*log(x)+_ + y(x)*x**3-x*log(x)-x**2)/(-log(1/x)+exp(x))/x) +--R +--R +--R (46) +--R 2 2 1 x 3 2 2 +--R (x y(x) - x y(x))log(x) - y(x)log(-) + y(x)%e + x y(x) - x y(x) +--R , x +--R y (x)= ------------------------------------------------------------------ +--R 1 x +--R x log(-) - x %e +--R x +--R Type: Equation Expression Integer +--E 46 + +--S 47 of 97 +solve(ode714,y,x) +--R +--R +--R (47) +--R - +--I 1 %I 2 +--I x %I log(%I) + log(--) - %e + %I +--I ++ %I +--I | --------------------------------- d%I +--I ++ 1 %I +--I %I log(--) - %I %e +--I %I +--R y(x)%e +--R * +--R INTSIGN +--R , +--R x +--R , +--R 2 +--I - %I log(%I) - %I +--R -------------------------------------------------------------- +--I 1 %I 2 +--I %I %I log(%I) + log(--) - %e + %I +--I ++ %I +--I | --------------------------------- d%I +--I ++ 1 %I +--I %I log(--) - %I %e +--I 1 %I %I +--R (log(--) - %e )%e +--I %I +--R * +--I d%I +--R + +--R 1 +--R / +--I 1 %I 2 +--I x %I log(%I) + log(--) - %e + %I +--I ++ %I +--I | --------------------------------- d%I +--I ++ 1 %I +--I %I log(--) - %I %e +--I %I +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 47 + +--S 48 of 97 +ode719 := (D(y(x),x) = y(x)*(-exp(x)+log(2*x)*x**2*y(x)-log(2*x)*x)/x/exp(x)) +--R +--R +--R 2 2 x +--R , (x y(x) - x y(x))log(2x) - y(x)%e +--R (48) y (x)= ----------------------------------- +--R x +--R x %e +--R Type: Equation Expression Integer +--E 48 + +--S 49 of 97 +solve(ode719,y,x) +--R +--R +--R - x y(x) + 1 +--R (49) ---------------------------------- +--I x %I +--I ++ %I log(2%I) + %e +--I | ------------------ d%I +--I ++ %I +--I %I %e +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 49 + +--S 50 of 97 +ode736 := (D(y(x),x) = (2*x**2+2*x+x**4-2*y(x)*x**2-1+y(x)**2)/(x+1)) +--R +--R +--R 2 2 4 2 +--R , y(x) - 2x y(x) + x + 2x + 2x - 1 +--R (50) y (x)= ----------------------------------- +--R x + 1 +--R Type: Equation Expression Integer +--E 50 + +--S 51 of 97 +solve(ode736,y,x) +--R +--R +--R 2 4 3 2 +--R (x + 2x - 2)y(x) - x - 2x + 3x + 2x + 4 +--R (51) ------------------------------------------- +--R 2 +--R 2y(x) - 2x - 2 +--R Type: Union(Expression Integer,...) +--E 51 + +--S 52 of 97 +ode765 := (D(y(x),x) = y(x)*(-1-log((x-1)*(1+x)/x)+_ + log((x-1)*(1+x)/x)*x*y(x))/x) +--R +--R +--R 2 +--R 2 x - 1 +--R (x y(x) - y(x))log(------) - y(x) +--R , x +--R (52) y (x)= ---------------------------------- +--R x +--R Type: Equation Expression Integer +--E 52 + +--S 53 of 97 +solve(ode765,y,x) +--R +--R +--R - x y(x) + 1 +--R (53) -------------------------------- +--R 2 +--I %I - 1 +--R x log(-------) + 1 +--I ++ %I +--I | ---------------- d%I +--I ++ %I +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 53 + +--S 54 of 97 +ode766 := (D(y(x),x) = y(x)*(-log(x)-x*log((x-1)*(1+x)/x)+_ + log((x-1)*(1+x)/x)*x**2*y(x))/x/log(x)) +--R +--R +--R 2 +--R 2 2 x - 1 +--R - y(x)log(x) + (x y(x) - x y(x))log(------) +--R , x +--R (54) y (x)= -------------------------------------------- +--R x log(x) +--R Type: Equation Expression Integer +--E 54 + +--S 55 of 97 +solve(ode766,y,x) +--R +--R +--R (55) +--R - +--R 2 +--I %I - 1 +--I x log(%I) + %I log(-------) +--I ++ %I +--I | ------------------------- d%I +--I ++ %I log(%I) +--R y(x)%e +--R * +--R 2 +--I %I - 1 +--I x %I log(-------) +--I ++ %I +--I | - --------------------------------------------- d%I +--R ++ 2 +--I %I - 1 +--I %I log(%I) + %I log(-------) +--I ++ %I +--I | ------------------------- d%I +--I ++ %I log(%I) +--I log(%I)%e +--R + +--R 1 +--R / +--R 2 +--I %I - 1 +--I x log(%I) + %I log(-------) +--I ++ %I +--I | ------------------------- d%I +--I ++ %I log(%I) +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 55 + +--S 56 of 97 +ode776 := (D(y(x),x) = y(x)*(-log(1/x)-log((x**2+1)/x)*x+_ + log((x**2+1)/x)*x**2*y(x))/x/log(1/x)) +--R +--R +--R 2 +--R 2 2 x + 1 1 +--R (x y(x) - x y(x))log(------) - y(x)log(-) +--R , x x +--R (56) y (x)= ------------------------------------------ +--R 1 +--R x log(-) +--R x +--R Type: Equation Expression Integer +--E 56 + +--S 57 of 97 +solve(ode776,y,x) +--R +--R +--R - x y(x) + 1 +--R (57) ----------------------------------------- +--R 2 +--I %I + 1 1 +--I x %I log(-------) + log(--) +--I ++ %I %I +--I | ------------------------- d%I +--R ++ 1 +--I %I log(--) +--I %I +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 57 + +--S 58 of 97 +ode872 := (D(y(x),x) = 1/5*(-30*y(x)*x**3+12*x**6+70*x**(7/2)-30*x**3-_ + 25*y(x)*x**(1/2)+50*x-25*x**(1/2)-25)/_ + (-5*y(x)+2*x**3+10*x**(1/2)-5)/x) +--R +--R +--R 3 +-+ 3 6 3 +--R , (- 25y(x) + 70x - 25)\|x - 30x y(x) + 12x - 30x + 50x - 25 +--R (58) y (x)= -------------------------------------------------------------- +--R +-+ 4 +--R 50x\|x - 25x y(x) + 10x - 25x +--R Type: Equation Expression Integer +--E 58 + +--S 59 of 97 +solve(ode872,y,x) +--R +--R +--R (59) +--R +-+ 3 +-+ 2 3 +--R 100log(\|x ) + (100y(x) - 40x + 100)\|x - 25y(x) + (20x - 50)y(x) +--R + +--R 6 3 +--R - 4x + 20x - 100x +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 59 + +--S 60 of 97 +ode555 := sqrt(D(y(x),x)**2+1)+x*D(y(x),x)-y(x) +--R +--R +--R +----------+ +--R | , 2 , +--R (60) |y (x) + 1 + xy (x) - y(x) +--R \| +--R Type: Expression Integer +--E 60 + +--S 61 of 97 +solve(ode555,y,x) +--R +--R +--R +-----------+ +--R | , 2 +--I x |y (%I) + 1 - y(x) +--R ++ \| +--I (61) | --------------------- d%I +--R ++ 2 +--I %I +--R Type: Union(Expression Integer,...) +--E 61 + +--S 62 of 97 +ode557 := x*(sqrt(D(y(x),x)**2+1)+D(y(x),x))-y(x) +--R +--R +--R +----------+ +--R | , 2 , +--R (62) x |y (x) + 1 + xy (x) - y(x) +--R \| +--R Type: Expression Integer +--E 62 + +--S 63 of 97 +solve(ode557,y,x) +--R +--R +--R +-----------+ +--R | , 2 +--I x %I |y (%I) + 1 - y(x) +--R ++ \| +--I (63) | ----------------------- d%I +--R ++ 2 +--I %I +--R Type: Union(Expression Integer,...) +--E 63 + +--S 64 of 97 +ode558 := a*x*sqrt(D(y(x),x)**2+1)+x*D(y(x),x)-y(x) +--R +--R +--R +----------+ +--R | , 2 , +--R (64) a x |y (x) + 1 + xy (x) - y(x) +--R \| +--R Type: Expression Integer +--E 64 + +--S 65 of 97 +solve(ode558,y,x) +--R +--R +--R +-----------+ +--R | , 2 +--I x %I a |y (%I) + 1 - y(x) +--R ++ \| +--I (65) | ------------------------- d%I +--R ++ 2 +--I %I +--R Type: Union(Expression Integer,...) +--E 65 + +--S 66 of 97 +ode562 := a*(D(y(x),x)**3+1)**(1/3)+b*x*D(y(x),x)-y(x) +--R +--R +--R +----------+ +--R | , 3 , +--R (66) a 3|y (x) + 1 + b xy (x) - y(x) +--R \| +--R Type: Expression Integer +--E 66 + +--S 67 of 97 +solve(ode562,y,x) +--R +--R +--I log(%I) log(%I) +--R - ------- +-----------+ - ------- +--R b | , 3 b +--I x a %e 3|y (%I) + 1 - y(x)%e +--R ++ \| +--I (67) | --------------------------------------------- d%I +--I ++ %I +--R Type: Union(Expression Integer,...) +--E 67 + +--S 68 of 97 +ode563 := log(D(y(x),x))+x*D(y(x),x)+a*y(x)+b +--R +--R +--R , , +--R (68) log(y (x)) + xy (x) + a y(x) + b +--R +--R Type: Expression Integer +--E 68 + +--S 69 of 97 +solve(ode563,y,x) +--R +--R +--I a log(%I) , a log(%I) +--I x %e log(y (%I)) + (a y(x) + b)%e +--R ++ +--I (69) | ------------------------------------------------ d%I +--I ++ %I +--R Type: Union(Expression Integer,...) +--E 69 + +--S 70 of 97 +ode564 := log(D(y(x),x))+a*(x*D(y(x),x)-y(x)) +--R +--R +--R , , +--R (70) log(y (x)) + a xy (x) - a y(x) +--R +--R Type: Expression Integer +--E 70 + +--S 71 of 97 +solve(ode564,y,x) +--R +--R +--R , +--I x log(y (%I)) - a y(x) +--R ++ +--I (71) | -------------------- d%I +--R ++ 2 +--I %I +--R Type: Union(Expression Integer,...) +--E 71 + +--S 72 of 97 +ode571 := a*x**n*f(D(y(x),x))+x*D(y(x),x)-y(x) +--R +--R +--R n , , +--R (72) a x f(y (x)) + xy (x) - y(x) +--R +--R Type: Expression Integer +--E 72 + +--S 73 of 97 +solve(ode571,y,x) +--R +--R +--R n , +--I x a %I f(y (%I)) - y(x) +--R ++ +--I (73) | --------------------- d%I +--R ++ 2 +--I %I +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 97 +ode573 := f(x*D(y(x),x)**2)+2*x*D(y(x),x)-y(x) +--R +--R +--R , 2 , +--R (74) f(x y (x) ) + 2xy (x) - y(x) +--R +--R Type: Expression Integer +--E 74 + +--S 75 of 97 +solve(ode573,y,x) +--R +--R +--R , 2 +--I x f(%I y (%I) ) - y(x) +--R ++ +--I (75) | -------------------- d%I +--R ++ +--+ +--I %I\|%I +--R Type: Union(Expression Integer,...) +--E 75 + +--S 76 of 97 +ode683 := (D(y(x),x) = y(x)*(-1+log(x*(x+1))*y(x)*x**4-log(x*(x+1))*x**3)/x) +--R +--R +--R 4 2 3 2 +--R , (x y(x) - x y(x))log(x + x) - y(x) +--R (76) y (x)= ------------------------------------ +--R x +--R Type: Equation Expression Integer +--E 76 + +--S 77 of 97 +solve(ode683,y,x) +--R +--R +--R - x y(x) + 1 +--R (77) ----------------------------------------------- +--R 3 2 3 2 +--R 6x log(x + x) - 4x + 3x - 6x +--R ------------------------------- +--R 3+-----+ 18 +--R x y(x)\|x + 1 %e +--R Type: Union(Expression Integer,...) +--E 77 + +--S 78 of 97 +ode703 := (D(y(x),x) = y(x)*(1-x+y(x)*x**2*log(x)+y(x)*x**3-x*log(x)-x**2)/_ + (x-1)/x) +--R +--R +--R 2 2 3 2 2 +--R , (x y(x) - x y(x))log(x) + x y(x) + (- x - x + 1)y(x) +--R (78) y (x)= ------------------------------------------------------- +--R 2 +--R x - x +--R Type: Equation Expression Integer +--E 78 + +--S 79 of 97 +solve(ode703,y,x) +--R +--R +--R - x y(x) + 1 +--R (79) ---------------------------- +--R 2 - dilog(x) + x +--R (x - x)y(x)%e +--R Type: Union(Expression Integer,...) +--E 79 + +--S 80 of 97 +ode714 := (D(y(x),x) = -y(x)*(-log(1/x)+exp(x)+y(x)*x**2*log(x)+_ + y(x)*x**3-x*log(x)-x**2)/(-log(1/x)+exp(x))/x) +--R +--R +--R (80) +--R 2 2 1 x 3 2 2 +--R (x y(x) - x y(x))log(x) - y(x)log(-) + y(x)%e + x y(x) - x y(x) +--R , x +--R y (x)= ------------------------------------------------------------------ +--R 1 x +--R x log(-) - x %e +--R x +--R Type: Equation Expression Integer +--E 80 + +--S 81 of 97 +solve(ode714,y,x) +--R +--R +--R (81) +--R - +--I 1 %I 2 +--I x %I log(%I) + log(--) - %e + %I +--I ++ %I +--I | --------------------------------- d%I +--I ++ 1 %I +--I %I log(--) - %I %e +--I %I +--R y(x)%e +--R * +--R INTSIGN +--R , +--R x +--R , +--R 2 +--I - %I log(%I) - %I +--R -------------------------------------------------------------- +--I 1 %I 2 +--I %I %I log(%I) + log(--) - %e + %I +--I ++ %I +--I | --------------------------------- d%I +--I ++ 1 %I +--I %I log(--) - %I %e +--I 1 %I %I +--R (log(--) - %e )%e +--I %I +--R * +--I d%I +--R + +--R 1 +--R / +--I 1 %I 2 +--I x %I log(%I) + log(--) - %e + %I +--I ++ %I +--I | --------------------------------- d%I +--I ++ 1 %I +--I %I log(--) - %I %e +--I %I +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 81 + +--S 82 of 97 +ode719 := (D(y(x),x) = y(x)*(-exp(x)+log(2*x)*x**2*y(x)-log(2*x)*x)/x/exp(x)) +--R +--R +--R 2 2 x +--R , (x y(x) - x y(x))log(2x) - y(x)%e +--R (82) y (x)= ----------------------------------- +--R x +--R x %e +--R Type: Equation Expression Integer +--E 82 + +--S 83 of 97 +solve(ode719,y,x) +--R +--R +--R - x y(x) + 1 +--R (83) ---------------------------------- +--I x %I +--I ++ %I log(2%I) + %e +--I | ------------------ d%I +--I ++ %I +--I %I %e +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 of 97 +ode736 := (D(y(x),x) = (2*x**2+2*x+x**4-2*y(x)*x**2-1+y(x)**2)/(x+1)) +--R +--R +--R 2 2 4 2 +--R , y(x) - 2x y(x) + x + 2x + 2x - 1 +--R (84) y (x)= ----------------------------------- +--R x + 1 +--R Type: Equation Expression Integer +--E 84 + +--S 85 of 97 +solve(ode736,y,x) +--R +--R +--R 2 4 3 2 +--R (x + 2x - 2)y(x) - x - 2x + 3x + 2x + 4 +--R (85) ------------------------------------------- +--R 2 +--R 2y(x) - 2x - 2 +--R Type: Union(Expression Integer,...) +--E 85 + +--S 86 of 97 +ode765 := (D(y(x),x) = y(x)*(-1-log((x-1)*(1+x)/x)+_ + log((x-1)*(1+x)/x)*x*y(x))/x) +--R +--R +--R 2 +--R 2 x - 1 +--R (x y(x) - y(x))log(------) - y(x) +--R , x +--R (86) y (x)= ---------------------------------- +--R x +--R Type: Equation Expression Integer +--E 86 + +--S 87 of 97 +solve(ode765,y,x) +--R +--R +--R - x y(x) + 1 +--R (87) -------------------------------- +--R 2 +--I %I - 1 +--R x log(-------) + 1 +--I ++ %I +--I | ---------------- d%I +--I ++ %I +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 87 + +--S 88 of 97 +ode766 := (D(y(x),x) = y(x)*(-log(x)-x*log((x-1)*(1+x)/x)+_ + log((x-1)*(1+x)/x)*x**2*y(x))/x/log(x)) +--R +--R +--R 2 +--R 2 2 x - 1 +--R - y(x)log(x) + (x y(x) - x y(x))log(------) +--R , x +--R (88) y (x)= -------------------------------------------- +--R x log(x) +--R Type: Equation Expression Integer +--E 88 + +--S 89 of 97 +solve(ode766,y,x) +--R +--R +--R (89) +--R - +--R 2 +--I %I - 1 +--I x log(%I) + %I log(-------) +--I ++ %I +--I | ------------------------- d%I +--I ++ %I log(%I) +--R y(x)%e +--R * +--R 2 +--I %I - 1 +--I x %I log(-------) +--I ++ %I +--I | - --------------------------------------------- d%I +--R ++ 2 +--I %I - 1 +--I %I log(%I) + %I log(-------) +--I ++ %I +--I | ------------------------- d%I +--I ++ %I log(%I) +--I log(%I)%e +--R + +--R 1 +--R / +--R 2 +--I %I - 1 +--I x log(%I) + %I log(-------) +--I ++ %I +--I | ------------------------- d%I +--I ++ %I log(%I) +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 89 + +--S 90 of 97 +ode776 := (D(y(x),x) = y(x)*(-log(1/x)-log((x**2+1)/x)*x+_ + log((x**2+1)/x)*x**2*y(x))/x/log(1/x)) +--R +--R +--R 2 +--R 2 2 x + 1 1 +--R (x y(x) - x y(x))log(------) - y(x)log(-) +--R , x x +--R (90) y (x)= ------------------------------------------ +--R 1 +--R x log(-) +--R x +--R Type: Equation Expression Integer +--E 90 + +--S 91 of 97 +solve(ode776,y,x) +--R +--R +--R - x y(x) + 1 +--R (91) ----------------------------------------- +--R 2 +--I %I + 1 1 +--I x %I log(-------) + log(--) +--I ++ %I %I +--I | ------------------------- d%I +--R ++ 1 +--I %I log(--) +--I %I +--R y(x)%e +--R Type: Union(Expression Integer,...) +--E 91 + +--S 92 of 97 +ode872 := (D(y(x),x) = 1/5*(-30*y(x)*x**3+12*x**6+70*x**(7/2)-30*x**3-_ + 25*y(x)*x**(1/2)+50*x-25*x**(1/2)-25)/(-5*y(x)+2*x**3+_ + 10*x**(1/2)-5)/x) +--R +--R +--R 3 +-+ 3 6 3 +--R , (- 25y(x) + 70x - 25)\|x - 30x y(x) + 12x - 30x + 50x - 25 +--R (92) y (x)= -------------------------------------------------------------- +--R +-+ 4 +--R 50x\|x - 25x y(x) + 10x - 25x +--R Type: Equation Expression Integer +--E 92 + +--S 93 of 97 +solve(ode872,y,x) +--R +--R +--R (93) +--R +-+ 3 +-+ 2 3 +--R 100log(\|x ) + (100y(x) - 40x + 100)\|x - 25y(x) + (20x - 50)y(x) +--R + +--R 6 3 +--R - 4x + 20x - 100x +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 93 + +--S 94 of 97 +ode956 := (D(y(x),x) = 1/(1+log(x))*y(x)*(-1-x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*x**2-x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*x**2*log(x)+x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*x**2*y(x)+2*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*x**2*y(x)*log(x)+x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*x**2*y(x)*log(x)**2)/x) +--R +--R +--R (94) +--R , +--R y (x) = +--R +--R 2 2 2 2 2 2 2 2 2 +--R (x y(x) log(x) + (2x y(x) - x y(x))log(x) + x y(x) - x y(x)) +--R * +--R 2 +--R 2log(x) 2 +--R ---------- ---------- +--R log(x) + 1 log(x) + 1 +--R %e x +--R + +--R - y(x) +--R / +--R x log(x) + x +--R Type: Equation Expression Integer +--E 94 + +--S 95 of 97 +solve(ode956,y,x) +--R +--R +--R - y(x)log(x) - y(x) + 1 +--R (95) ------------------------- +--R 4 4 +--R x x +--R -- -- +--R 4 4 +--R y(x)%e log(x) + y(x)%e +--R Type: Union(Expression Integer,...) +--E 95 + +--S 96 of 97 +ode957 := (D(y(x),x) = 1/(1+log(x))*y(x)*(-1-x**3*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)-x**3*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*log(x)+x**3*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*y(x)+2*x**3*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*y(x)*log(x)+x**3*x**(2/(1+log(x)))*_ + exp(2/(1+log(x))*log(x)**2)*y(x)*log(x)**2)/x) +--R +--R +--R (96) +--R , +--R y (x) = +--R +--R 3 2 2 3 2 3 3 2 3 +--R (x y(x) log(x) + (2x y(x) - x y(x))log(x) + x y(x) - x y(x)) +--R * +--R 2 +--R 2log(x) 2 +--R ---------- ---------- +--R log(x) + 1 log(x) + 1 +--R %e x +--R + +--R - y(x) +--R / +--R x log(x) + x +--R Type: Equation Expression Integer +--E 96 + +--S 97 of 97 +solve(ode957,y,x) +--R +--R +--R - y(x)log(x) - y(x) + 1 +--R (97) ------------------------- +--R 5 5 +--R x x +--R -- -- +--R 5 5 +--R y(x)%e log(x) + y(x)%e +--R Type: Union(Expression Integer,...) +--E 97 +)spool +)lisp (bye) +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} {\bf http://www.cs.uwaterloo.ca/$\tilde{}$ecterrab/odetools.html} +\end{thebibliography} +\end{document}