diff --git a/changelog b/changelog index 21958ab..46dc9dc 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,5 @@ +20071004 tpd src/input/Makefile kamke0.input regression test added +20071004 tpd src/input/kamke0.input ODE regression test added 20071001 tpd src/algebra/exposed.lisp add (|AxiomServer| . AXSERV) to basic 20071001 tpd src/algebra/Makefile add axserver.spad 20071001 acr src/algebra/axserver.spad axserver socket connection code diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index f62095a..c1ade3e 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -322,6 +322,7 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress alist.regress \ intmix2.regress intmix.regress int.regress intrf.regress \ iprntpk.regress \ ipftest.regress is.regress isprime.regress kafile.regress \ + kamke0.regress \ kernel.regress knot2.regress kovacic.regress kuipers.regress \ laplace.regress leg.regress limit.regress lindep.regress \ list.regress lode.regress lodesys.regress lodo1.regress \ @@ -556,11 +557,12 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input ${OUT}/algfacob.input \ ${OUT}/images3.input ${OUT}/images6.input ${OUT}/images6a.input \ ${OUT}/images7.input ${OUT}/images7a.input ${OUT}/infprod.input \ ${OUT}/intaf.input ${OUT}/intbypart.input \ - ${OUT}/intdeq.input ${OUT}/intef.input \ + ${OUT}/intdeq.input ${OUT}/intef.input \ ${OUT}/intg0.input ${OUT}/intheory.input ${OUT}/int.input \ ${OUT}/intlf.input ${OUT}/intmix.input ${OUT}/intrf.input \ ${OUT}/ipftest.input ${OUT}/is.input ${OUT}/isprime.input \ - ${OUT}/kafile.input ${OUT}/kernel.input ${OUT}/knot.input \ + ${OUT}/kafile.input ${OUT}/kamke0.input \ + ${OUT}/kernel.input ${OUT}/knot.input \ ${OUT}/kovacic.input ${OUT}/kuipers.input \ ${OUT}/laplace.input ${OUT}/leg.input ${OUT}/lexp.input \ ${OUT}/lextripk.input ${OUT}/lib.input ${OUT}/limit.input \ @@ -825,6 +827,7 @@ DOCFILES= \ ${DOC}/intmix.input.dvi ${DOC}/intrf.input.dvi \ ${DOC}/ipftest.input.dvi ${DOC}/is.input.dvi \ ${DOC}/isprime.input.dvi ${DOC}/kafile.input.dvi \ + ${DOC}/kamke0.input.dvi \ ${DOC}/kernel.input.dvi ${DOC}/knot2.input.dvi \ ${DOC}/knot.input.dvi ${DOC}/knownbugs.input.dvi \ ${DOC}/kovacic.input.dvi ${DOC}/kuipers.input.dvi \ diff --git a/src/input/kamke0.input.pamphlet b/src/input/kamke0.input.pamphlet new file mode 100644 index 0000000..d1a9d8b --- /dev/null +++ b/src/input/kamke0.input.pamphlet @@ -0,0 +1,1904 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input kamke0.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This is the first 50 of the Kamke test suite as published by +E. S. Cheb-Terrab\cite{1}. They have been rewritten using Axiom +syntax. Where possible we show that the particular solution actually +satisfies the original ordinary differential equation. +\end{abstract} +\eject +\tableofcontents +\eject +<<*>>= +)spool kamke0.output +)set break resume +)set mes auto off +)clear all + +--S 1 of 134 +y:=operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 1 + +--S 2 of 134 +f := operator 'f +--R +--R (2) f +--R Type: BasicOperator +--E 2 + +--S 3 of 134 +g := operator 'g +--R +--R (3) g +--R Type: BasicOperator +--E 3 + +--S 4 of 134 +ode1 := D(y(x),x) - (a4*x**4+a3*x**3+a2*x**2+a1*x+a0)**(-1/2) +--R +--R +--R +---------------------------------+ +--R | 4 3 2 , +--R \|a4 x + a3 x + a2 x + a1 x + a0 y (x) - 1 +--R +--R (4) --------------------------------------------- +--R +---------------------------------+ +--R | 4 3 2 +--R \|a4 x + a3 x + a2 x + a1 x + a0 +--R Type: Expression Integer +--E 4 + +--S 5 of 134 +ode1a:=solve(ode1,y,x) +--R +--R +--R (5) +--R x +--R ++ 1 +--I [particular= | ------------------------------------- d%N ,basis= [1]] +--R ++ +----------------------------------+ +--R | 4 3 2 +--I \|%N a4 + %N a3 + %N a2 + %N a1 + a0 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 5 + +--S 6 of 134 +ode2 := D(y(x),x) + a*y(x) - c*exp(b*x) +--R +--R +--R , b x +--R (6) y (x) - c %e + a y(x) +--R +--R Type: Expression Integer +--E 6 + +--S 7 of 134 +ode2a:=solve(ode2,y,x) +--R +--R +--R b x +--R c %e - a x +--R (7) [particular= -------,basis= [%e ]] +--R b + a +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 7 + +--S 8 of 134 +yx:=ode2a.particular +--R +--R b x +--R c %e +--R (8) ------- +--R b + a +--R Type: Expression Integer +--E 8 + +--S 9 of 134 +ode2expr:=D(yx,x) + a*yx -c*exp(b*x) +--R +--R (9) 0 +--R Type: Expression Integer +--E 9 + +--S 10 of 134 +ode3 := D(y(x),x) + a*y(x) - b*sin(c*x) +--R +--R , +--R (10) y (x) - b sin(c x) + a y(x) +--R +--R Type: Expression Integer +--E 10 + +--S 11 of 134 +ode3a:=solve(ode3,y,x) +--R +--R a b sin(c x) - b c cos(c x) - a x +--R (11) [particular= ---------------------------,basis= [%e ]] +--R 2 2 +--R c + a +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 11 + +--S 12 of 134 +yx:=ode3a.particular +--R +--R a b sin(c x) - b c cos(c x) +--R (12) --------------------------- +--R 2 2 +--R c + a +--R Type: Expression Integer +--E 12 + +--S 13 of 134 +ode3expr:=D(yx,x) + a*yx - b*sin(c*x) +--R +--R (13) 0 +--R Type: Expression Integer +--E 13 + +--S 14 of 134 +ode4 := D(y(x),x) + 2*x*y(x) - x*exp(-x**2) +--R +--R 2 +--R , - x +--R (14) y (x) - x %e + 2x y(x) +--R +--R Type: Expression Integer +--E 14 + +--S 15 of 134 +ode4a:=solve(ode4,y,x) +--R +--R 2 +--R 2 - x 2 +--R x %e - x +--R (15) [particular= --------,basis= [%e ]] +--R 2 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 15 + +--S 16 of 134 +yx:=ode4a.particular +--R +--R 2 +--R 2 - x +--R x %e +--R (16) -------- +--R 2 +--R Type: Expression Integer +--E 16 + +--S 17 of 134 +ode4expr:=D(yx,x) + 2*x*yx - x*exp(-x**2) +--R +--R (17) 0 +--R Type: Expression Integer +--E 17 + +--S 18 of 134 +ode5 := D(y(x),x) + y(x)*cos(x) - exp(2*x) +--R +--R , 2x +--R (18) y (x) - %e + y(x)cos(x) +--R +--R Type: Expression Integer +--E 18 + +--S 19 of 134 +ode5a:=solve(ode5,y,x) +--R +--I x 2%H +--R - sin(x) ++ %e - sin(x) +--I (19) [particular= %e | ----------- d%H ,basis= [%e ]] +--I ++ - sin(%H) +--R %e +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 19 + +--S 20 of 134 +ode6 := D(y(x),x) + y(x)*cos(x) - sin(2*x)/2 +--R +--R , +--R 2y (x) - sin(2x) + 2y(x)cos(x) +--R +--R (20) ------------------------------ +--R 2 +--R Type: Expression Integer +--E 20 + +--S 21 of 134 +ode6a:=solve(ode6,y,x) +--R +--R - sin(x) +--R (21) [particular= sin(x) - 1,basis= [%e ]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 21 + +--S 22 of 134 +yx:=ode6a.particular +--R +--R (22) sin(x) - 1 +--R Type: Expression Integer +--E 22 + +--S 23 of 134 +ode6expr:=D(yx,x) + yx*cos(x) - sin(2*x)/2 +--R +--R - sin(2x) + 2cos(x)sin(x) +--R (23) ------------------------- +--R 2 +--R Type: Expression Integer +--E 23 + +--S 24 of 134 +sin2rule := rule 2*cos(x)*sin(x) == sin(2*x) +--R +--I (24) 2%Y cos(x)sin(x) == %Y sin(2x) +--R Type: RewriteRule(Integer,Integer,Expression Integer) +--E 24 + +--S 25 of 134 +sin2rule ode6expr +--R +--R (25) 0 +--R Type: Expression Integer +--E 25 + +--S 26 of 134 +ode7 := D(y(x),x) + y(x)*cos(x) - exp(-sin(x)) +--R +--R , - sin(x) +--R (26) y (x) - %e + y(x)cos(x) +--R +--R Type: Expression Integer +--E 26 + +--S 27 of 134 +ode7a:=solve(ode7,y,x) +--R +--R - sin(x) - sin(x) +--R (27) [particular= x %e ,basis= [%e ]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 27 + +--S 28 of 134 +yx:=ode7a.particular +--R +--R - sin(x) +--R (28) x %e +--R Type: Expression Integer +--E 28 + +--S 29 of 134 +ode7expr := D(yx,x) + yx*cos(x) - exp(-sin(x)) +--R +--R (29) 0 +--R Type: Expression Integer +--E 29 + +--S 30 of 134 +ode8 := D(y(x),x) + y(x)*tan(x) - sin(2*x) +--R +--R , +--R (30) y (x) + y(x)tan(x) - sin(2x) +--R +--R Type: Expression Integer +--E 30 + +--S 31 of 134 +ode8a:=solve(ode8,y,x) +--R +--R (31) +--R +-------+ +--R 2 | 1 +--R (- 2cos(x) + 2cos(x)) |------- +--R 4| 4 +--R \|cos(x) 1 +--R [particular= --------------------------------,basis= [--------------]] +--R +-----------+ +-----------+ +--R | 2 | 2 +--R \|tan(x) + 1 \|tan(x) + 1 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 31 + +--S 32 of 134 +yx:=ode8a.particular +--R +--R +-------+ +--R 2 | 1 +--R (- 2cos(x) + 2cos(x)) |------- +--R 4| 4 +--R \|cos(x) +--R (32) -------------------------------- +--R +-----------+ +--R | 2 +--R \|tan(x) + 1 +--R Type: Expression Integer +--E 32 + +--S 33 of 134 +ode8expr:=D(yx,x) + yx*tan(x) - sin(2*x) +--R +--R +-------+3 +-----------+ +--R 3 | 1 | 2 +--R - cos(x) sin(2x) |------- \|tan(x) + 1 + 2sin(x) +--R 4| 4 +--R \|cos(x) +--R (33) --------------------------------------------------- +--R +-------+3 +-----------+ +--R 3 | 1 | 2 +--R cos(x) |------- \|tan(x) + 1 +--R 4| 4 +--R \|cos(x) +--R Type: Expression Integer +--E 33 + +--S 34 of 134 +ode9 := D(y(x),x) - (sin(log(x)) + cos(log(x)) +a)*y(x) +--R +--R , +--R (34) y (x) - y(x)sin(log(x)) - y(x)cos(log(x)) - a y(x) +--R +--R Type: Expression Integer +--E 34 + +--S 35 of 134 +ode9a:=solve(ode9,y,x) +--R +--R x sin(log(x)) + a x +--R (35) [particular= 0,basis= [%e ]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 35 + +--S 36 of 134 +yx:=ode9a.particular +--R +--R (36) 0 +--R Type: Expression Integer +--E 36 + +--S 37 of 134 +ode9expr:=D(yx,x) - (sin(log(x)) + cos(log(x)) +a)*yx +--R +--R (37) 0 +--R Type: Expression Integer +--E 37 + +--S 38 of 134 +ode10 := D(y(x),x) + D(f(x),x)*y(x) - f(x)*D(f(x),x) +--R +--R , , +--R (38) y (x) + (y(x) - f(x))f (x) +--R +--R Type: Expression Integer +--E 38 + +--S 39 of 134 +ode10a:=solve(ode10,y,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 39 + +--S 40 of 134 +ode11 := D(y(x),x) + f(x)*y(x) - g(x) +--R +--R , +--R (39) y (x) + f(x)y(x) - g(x) +--R +--R Type: Expression Integer +--E 40 + +--S 41 of 134 +ode11a:=solve(ode11,y,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 41 + +--S 42 of 134 +ode12 := D(y(x),x) + y(x)**2 - 1 +--R +--R , 2 +--R (40) y (x) + y(x) - 1 +--R +--R Type: Expression Integer +--E 42 + +--S 43 of 134 +yx:=solve(ode12,y,x) +--R +--R - log(y(x) + 1) + log(y(x) - 1) + 2x +--R (41) ------------------------------------ +--R 2 +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 134 +ode12expr:=D(yx,x) + yx**2 - 1 +--R +--R (42) +--R , 2 2 +--R 4y (x) + (y(x) - 1)log(y(x) + 1) +--R +--R + +--R 2 2 +--R ((- 2y(x) + 2)log(y(x) - 1) - 4x y(x) + 4x)log(y(x) + 1) +--R + +--R 2 2 2 2 2 2 +--R (y(x) - 1)log(y(x) - 1) + (4x y(x) - 4x)log(y(x) - 1) + 4x y(x) - 4x +--R / +--R 2 +--R 4y(x) - 4 +--R Type: Expression Integer +--E 44 + +--S 45 of 134 +ode13 := D(y(x),x) + y(x)**2 - a*x - b +--R +--R , 2 +--R (43) y (x) + y(x) - a x - b +--R +--R Type: Expression Integer +--E 45 + +--S 46 of 134 +ode13a:=solve(ode13,y,x) +--R +--R (44) "failed" +--R Type: Union("failed",...) +--E 46 + +--S 47 of 134 +ode14 := D(y(x),x) + y(x)**2 + a*x**m +--R +--R +--R , m 2 +--R (45) y (x) + a x + y(x) +--R +--R Type: Expression Integer +--E 47 + +--S 48 of 134 +ode14a:=solve(ode14,y,x) +--R +--R (46) "failed" +--R Type: Union("failed",...) +--E 48 + +--S 49 of 134 +ode15 := D(y(x),x) + y(x)**2 - 2*x**2*y(x) + x**4 -2*x-1 +--R +--R +--R , 2 2 4 +--R (47) y (x) + y(x) - 2x y(x) + x - 2x - 1 +--R +--R Type: Expression Integer +--E 49 + +--S 50 of 134 +yx:=solve(ode15,y,x) +--R +--R 2 +--R y(x) - x + 1 +--R (48) --------------------- +--R 2 2x +--R (2y(x) - 2x - 2)%e +--R Type: Union(Expression Integer,...) +--E 50 + +--S 51 of 134 +ode15expr:=D(yx,x) + yx**2 - 2*x**2*yx + x**4 -2*x-1 +--R +--R (49) +--R 2x , +--R - 4%e y (x) +--R +--R + +--R 4 2 6 4 3 2 8 +--R (4x - 8x - 4)y(x) + (- 8x - 8x + 16x + 8x + 16x + 8)y(x) + 4x +--R + +--R 6 5 3 2 +--R 8x - 8x - 16x - 8x - 8x - 4 +--R * +--R 2x 2 +--R (%e ) +--R + +--R 2 2 4 2 6 4 2 2x +--R ((- 4x - 4)y(x) + (8x + 8x )y(x) - 4x - 4x + 4x + 8x + 4)%e +--R + +--R 2 2 4 2 +--R y(x) + (- 2x + 2)y(x) + x - 2x + 1 +--R / +--R 2 2 4 2 2x 2 +--R (4y(x) + (- 8x - 8)y(x) + 4x + 8x + 4)(%e ) +--R Type: Expression Integer +--E 51 + +--S 52 of 134 +ode16 := D(y(x),x) + y(x)**2 +(x*y(x)-1)*f(x) +--R +--R , 2 +--R (50) y (x) + y(x) + x f(x)y(x) - f(x) +--R +--R Type: Expression Integer +--E 52 + +--S 53 of 134 +ode16a:=solve(ode16,y,x) +--R +--R (51) "failed" +--R Type: Union("failed",...) +--E 53 + +--S 54 of 134 +ode17 := D(y(x),x) - y(x)**2 -3*y(x) + 4 +--R +--R +--R , 2 +--R (52) y (x) - y(x) - 3y(x) + 4 +--R +--R Type: Expression Integer +--E 54 + +--S 55 of 134 +yx:=solve(ode17,y,x) +--R +--R +--R - log(y(x) + 4) + log(y(x) - 1) - 5x +--R (53) ------------------------------------ +--R 5 +--R Type: Union(Expression Integer,...) +--E 55 + +--S 56 of 134 +ode17expr:=D(yx,x) - yx**2 -3*yx + 4 +--R +--R (54) +--R , 2 2 +--R 25y (x) + (- y(x) - 3y(x) + 4)log(y(x) + 4) +--R +--R + +--R 2 2 +--R (2y(x) + 6y(x) - 8)log(y(x) - 1) + (- 10x + 15)y(x) +--R + +--R (- 30x + 45)y(x) + 40x - 60 +--R * +--R log(y(x) + 4) +--R + +--R 2 2 +--R (- y(x) - 3y(x) + 4)log(y(x) - 1) +--R + +--R 2 +--R ((10x - 15)y(x) + (30x - 45)y(x) - 40x + 60)log(y(x) - 1) +--R + +--R 2 2 2 2 +--R (- 25x + 75x + 75)y(x) + (- 75x + 225x + 225)y(x) + 100x - 300x - 300 +--R / +--R 2 +--R 25y(x) + 75y(x) - 100 +--R Type: Expression Integer +--E 56 + +--S 57 of 134 +ode18 := D(y(x),x) - y(x)**2 - x*y(x) - x + 1 +--R +--R +--R , 2 +--R (55) y (x) - y(x) - x y(x) - x + 1 +--R +--R Type: Expression Integer +--E 57 + +--S 58 of 134 +yx:=solve(ode18,y,x) +--R +--R +--R 2 +--R - x + 4x +--R --------- x +--R 2 ++ 1 +--I (- y(x) - 1)%e | - ------------- d%N + 1 +--R ++ 2 +--I - %N + 4%N +--R ----------- +--R 2 +--R %e +--R (56) ---------------------------------------------------- +--R 2 +--R - x + 4x +--R --------- +--R 2 +--R (y(x) + 1)%e +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 of 134 +ode18expr:=D(yx,x) - yx**2 - x*yx - x + 1 +--R (57) +--R 2 2 +--R - x + 4x +--R --------- x 2 +--R 2 2 ++ 1 +--I (- y(x) - 2y(x) - 1)(%e ) | - ------------- d%H +--R ++ 2 +--I - %H + 4%H +--R ----------- +--R 2 +--R %e +--R + +--R 2 2 2 +--R - x + 4x - x + 4x +--R --------- --------- +--R 2 2 2 +--R ((x y(x) + 2x y(x) + x)(%e ) + (2y(x) + 2)%e ) +--R * +--R x +--R ++ 1 +--I | - ------------- d%H +--R ++ 2 +--I - %H + 4%H +--R ----------- +--R 2 +--R %e +--R + +--R 2 +--R - x + 4x +--R --------- +--R 2 , +--R - %e y (x) +--R +--R + +--R 2 2 +--R - x + 4x +--R --------- +--R 2 2 +--R ((- x + 1)y(x) + (- 2x + 2)y(x) - x + 1)(%e ) +--R + +--R 2 +--R - x + 4x +--R --------- +--R 2 2 +--R (y(x) - 1)%e - 1 +--R / +--R 2 2 +--R - x + 4x +--R --------- +--R 2 2 +--R (y(x) + 2y(x) + 1)(%e ) +--R Type: Expression Integer +--E 59 + +--S 60 of 134 +ode19 := D(y(x),x) - (y(x) + x)**2 +--R +--R +--R , 2 2 +--R (58) y (x) - y(x) - 2x y(x) - x +--R +--R Type: Expression Integer +--E 60 + +--S 61 of 134 +yx:=solve(ode19,y,x) +--R +--R +--R +---+ +--R - y(x) + \|- 1 - x +--R (59) -------------------------------------- +--R +---+ +--R +---+ +---+ 2x\|- 1 +--R (2\|- 1 y(x) + 2x\|- 1 - 2)%e +--R Type: Union(Expression Integer,...) +--E 61 + +--S 62 of 134 +ode19expr := D(yx,x) - (yx + x)**2 +--R +--R (60) +--R +---+ +--R 2x\|- 1 , +--R - 4%e y (x) +--R +--R + +--R 2 2 2 +---+ 3 3 +---+ 4 2 +--R (- 4x y(x) + (- 8x \|- 1 - 8x )y(x) - 8x \|- 1 - 4x + 4x ) +--R * +--R +---+ 2 +--R 2x\|- 1 +--R (%e ) +--R + +--R +---+ 2 2 +---+ 3 +---+ +--R (- 4x\|- 1 + 4)y(x) + (- 8x \|- 1 + 8x)y(x) + (- 4x - 4x)\|- 1 +--R + +--R 2 +--R 4x +--R * +--R +---+ +--R 2x\|- 1 +--R %e +--R + +--R 2 +---+ +---+ 2 +--R y(x) + (- 2\|- 1 + 2x)y(x) - 2x\|- 1 + x - 1 +--R / +--R +---+ 2 +--R 2 +---+ +---+ 2 2x\|- 1 +--R (4y(x) + (8\|- 1 + 8x)y(x) + 8x\|- 1 + 4x - 4)(%e ) +--R Type: Expression Integer +--E 62 + +--S 63 of 134 +ode20 := D(y(x),x) - y(x)**2 +(x**2 + 1)*y(x) - 2*x +--R +--R +--R , 2 2 +--R (61) y (x) - y(x) + (x + 1)y(x) - 2x +--R +--R Type: Expression Integer +--E 63 + +--S 64 of 134 +yx:=solve(ode20,y,x) +--R +--R 3 +--R - x - 3x +--R --------- x +--R 2 3 ++ 1 +--I (- y(x) + x + 1)%e | - ------------- d%H + 1 +--R ++ 3 +--I - %H - 3%H +--R ----------- +--R 3 +--R %e +--R (62) --------------------------------------------------------- +--R 3 +--R - x - 3x +--R --------- +--R 2 3 +--R (y(x) - x - 1)%e +--R Type: Union(Expression Integer,...) +--E 64 + +--S 65 of 134 +ode20expr:=D(yx,x) - yx**2 +(x**2 + 1)*yx - 2*x +--R +--R (63) +--R 3 2 +--R - x - 3x +--R --------- +--R 2 2 4 2 3 +--R (- y(x) + (2x + 2)y(x) - x - 2x - 1)(%e ) +--R * +--R x 2 +--R ++ 1 +--I | - ------------- d%H +--R ++ 3 +--I - %H - 3%H +--R ----------- +--R 3 +--R %e +--R + +--R 2 2 4 2 6 4 2 +--R ((- x - 1)y(x) + (2x + 4x + 2)y(x) - x - 3x - 3x - 1) +--R * +--R 3 2 +--R - x - 3x +--R --------- +--R 3 +--R (%e ) +--R + +--R 3 +--R - x - 3x +--R --------- +--R 2 3 +--R (2y(x) - 2x - 2)%e +--R * +--R x +--R ++ 1 +--I | - ------------- d%H +--R ++ 3 +--I - %H - 3%H +--R ----------- +--R 3 +--R %e +--R + +--R 3 +--R - x - 3x +--R --------- +--R 3 , +--R - %e y (x) +--R +--R + +--R 3 2 +--R - x - 3x +--R --------- +--R 2 3 5 3 3 +--R (- 2x y(x) + (4x + 4x)y(x) - 2x - 4x - 2x)(%e ) +--R + +--R 3 +--R - x - 3x +--R --------- +--R 2 4 2 3 +--R (y(x) - x - 2x + 2x - 1)%e - 1 +--R / +--R 3 2 +--R - x - 3x +--R --------- +--R 2 2 4 2 3 +--R (y(x) + (- 2x - 2)y(x) + x + 2x + 1)(%e ) +--R Type: Expression Integer +--E 65 + +--S 66 of 134 +ode21 := D(y(x),x) - y(x)**2 +y(x)*sin(x) - cos(x) +--R +--R +--R , 2 +--R (64) y (x) + y(x)sin(x) - cos(x) - y(x) +--R +--R Type: Expression Integer +--E 66 + +--S 67 of 134 +ode21a:=solve(ode21,y,x) +--R +--R +--R (65) "failed" +--R Type: Union("failed",...) +--E 67 + +--S 68 of 134 +ode22 := D(y(x),x) - y(x)**2 -y(x)*sin(2*x) - cos(2*x) +--R +--R +--R , 2 +--R (66) y (x) - y(x)sin(2x) - cos(2x) - y(x) +--R +--R Type: Expression Integer +--E 68 + +--S 69 of 134 +ode22a:=solve(ode22,y,x) +--R +--R +--R (67) "failed" +--R Type: Union("failed",...) +--E 69 + +--S 70 of 134 +ode23 := D(y(x),x) + a*y(x)**2 - b +--R +--R +--R , 2 +--R (68) y (x) + a y(x) - b +--R +--R Type: Expression Integer +--E 70 + +--S 71 of 134 +yx:=solve(ode23,y,x) +--R +--R +--R 2 +---+ +--R (a y(x) + b)\|a b - 2a b y(x) +---+ +--R log(-------------------------------) + 2x\|a b +--R 2 +--R a y(x) - b +--R (69) ----------------------------------------------- +--R +---+ +--R 2\|a b +--R Type: Union(Expression Integer,...) +--E 71 + +--S 72 of 134 +ode23expr := D(yx,x) + a*yx**2 - b +--R +--R (70) +--R 2 +---+ 2 +--R , 2 (a y(x) + b)\|a b - 2a b y(x) +--R 4by (x) + (a y(x) - b)log(-------------------------------) +--R 2 +--R a y(x) - b +--R + +--R 2 +---+ +--R 2 +---+ (a y(x) + b)\|a b - 2a b y(x) +--R (4a x y(x) - 4b x)\|a b log(-------------------------------) +--R 2 +--R a y(x) - b +--R + +--R 2 2 2 2 2 2 3 2 +--R (4a b x - 4a b + 4a b)y(x) - 4a b x + 4b - 4b +--R / +--R 2 2 +--R 4a b y(x) - 4b +--R Type: Expression Integer +--E 72 + +--S 73 of 134 +ode24 := D(y(x),x) + a*y(x)**2 - b*x**nu +--R +--R +--R , nu 2 +--R (71) y (x) - b x + a y(x) +--R +--R Type: Expression Integer +--E 73 + +--S 74 of 134 +ode24a:=solve(ode24,y,x) +--R +--R +--R (72) "failed" +--R Type: Union("failed",...) +--E 74 + +--S 75 of 134 +ode25 := D(y(x),x) + a*y(x)**2 - b*x**(2*nu) - c*x**(nu-1) +--R +--R +--R , 2nu nu - 1 2 +--R (73) y (x) - b x - c x + a y(x) +--R +--R Type: Expression Integer +--E 75 + +--S 76 of 134 +ode25expr:=solve(ode25,y,x) +--R +--R +--R (74) "failed" +--R Type: Union("failed",...) +--E 76 + +--S 77 of 134 +ode26 := D(y(x),x) - (A*y(x) - a)*(B*y(x) - b) +--R +--R +--R , 2 +--R (75) y (x) - A B y(x) + (A b + B a)y(x) - a b +--R +--R Type: Expression Integer +--E 77 + +--S 78 of 134 +yx:=solve(ode26,y,x) +--R +--R +--R log(B y(x) - b) - log(A y(x) - a) + (- A b + B a)x +--R (76) -------------------------------------------------- +--R A b - B a +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 of 134 +ode26expr := D(yx,x) - (A*yx - a)*(B*yx - b) +--R +--R (77) +--R 2 2 2 2 , +--R (A b - 2A B a b + B a )y (x) +--R +--R + +--R 2 2 2 2 2 2 +--R (- A B y(x) + (A B b + A B a)y(x) - A B a b)log(B y(x) - b) +--R + +--R 2 2 2 2 2 +--R (2A B y(x) + (- 2A B b - 2A B a)y(x) + 2A B a b)log(A y(x) - a) +--R + +--R 3 2 2 3 3 2 3 2 2 +--R ((2A B b - 2A B a)x + A B b - A B a )y(x) +--R + +--R 3 2 3 2 3 3 2 2 2 2 3 3 +--R ((- 2A B b + 2A B a )x - A b - A B a b + A B a b + B a )y(x) +--R + +--R 2 2 2 2 2 3 2 3 +--R (2A B a b - 2A B a b)x + A a b - B a b +--R * +--R log(B y(x) - b) +--R + +--R 2 2 2 2 2 2 +--R (- A B y(x) + (A B b + A B a)y(x) - A B a b)log(A y(x) - a) +--R + +--R 3 2 2 3 3 2 3 2 2 +--R ((- 2A B b + 2A B a)x - A B b + A B a )y(x) +--R + +--R 3 2 3 2 3 3 2 2 2 2 3 3 +--R ((2A B b - 2A B a )x + A b + A B a b - A B a b - B a )y(x) +--R + +--R 2 2 2 2 2 3 2 3 +--R (- 2A B a b + 2A B a b)x - A a b + B a b +--R * +--R log(A y(x) - a) +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (- A B b + 2A B a b - A B a )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 3 3 +--R (- A B b + A B a b + A B a b - A B a )x - A B a b +--R + +--R 2 2 2 3 2 3 3 2 2 3 2 +--R (2A B a - A B)b + (- A B a + 2A B a)b - A B a +--R * +--R 2 +--R y(x) +--R + +--R 4 3 3 2 2 2 3 2 4 3 2 4 4 2 2 2 2 4 4 +--R (A B b - A B a b - A B a b + A B a )x + (A b - 2A B a b + B a )x +--R + +--R 3 4 2 2 3 3 2 3 2 2 3 4 2 2 +--R A a b + (- A B a + A )b + (- A B a - A B a)b + (B a - A B a )b +--R + +--R 3 3 +--R B a +--R * +--R y(x) +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- A B a b + 2A B a b - A B a b)x +--R + +--R 3 4 2 2 3 2 3 2 3 4 2 2 4 3 2 3 +--R (- A a b + A B a b + A B a b - B a b)x - A a b + (2A B a - A a)b +--R + +--R 2 4 2 2 2 3 +--R (- B a + 2A B a )b - B a b +--R / +--R 3 2 2 2 3 2 2 +--R (A B b - 2A B a b + A B a )y(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 2 2 2 3 +--R (- A b + A B a b + A B a b - B a )y(x) + A a b - 2A B a b + B a b +--R Type: Expression Integer +--E 79 + +--S 80 of 134 +ode27 := D(y(x),x) + a*y(x)*(y(x)-x) - 1 +--R +--R +--R , 2 +--R (78) y (x) + a y(x) - a x y(x) - 1 +--R +--R Type: Expression Integer +--E 80 + +--S 81 of 134 +ode27a:=solve(ode27,y,x) +--R +--R +--R 2 +--R a x +--R ---- x +--R 2 ++ a +--I (- y(x) + x)%e | ------ d%N + 1 +--R ++ 2 +--I %N a +--R ---- +--R 2 +--R %e +--R (79) -------------------------------------- +--R 2 +--R a x +--R ---- +--R 2 +--R (y(x) - x)%e +--R Type: Union(Expression Integer,...) +--E 81 + +--S 82 of 134 +ode28 := D(y(x),x) + x*y(x)**2 -x**3*y(x) - 2*x +--R +--R +--R , 2 3 +--R (80) y (x) + x y(x) - x y(x) - 2x +--R +--R Type: Expression Integer +--E 82 + +--S 83 of 134 +ode28a:=solve(ode28,y,x) +--R +--R +--R 4 +--R x +--R -- x +--I 2 4 ++ %N +--I (- y(x) + x )%e | ----- d%N + 1 +--R ++ 4 +--I %N +--R --- +--R 4 +--R %e +--R (81) ------------------------------------ +--R 4 +--R x +--R -- +--R 2 4 +--R (y(x) - x )%e +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 of 134 +ode29 := D(y(x),x) - x*y(x)**2 - 3*x*y(x) +--R +--R +--R , 2 +--R (82) y (x) - x y(x) - 3x y(x) +--R +--R Type: Expression Integer +--E 84 + +--S 85 of 134 +yx:=solve(ode29,y,x) +--R +--R +--R 2 +--R - 2log(y(x) + 3) + 2log(y(x)) - 3x +--R (83) ----------------------------------- +--R 6 +--R Type: Union(Expression Integer,...) +--E 85 + +--S 86 of 134 +ode29expr := D(yx,x) - x*yx**2 - 3*x*yx +--R +--R (84) +--R , 2 2 +--R 36y (x) + (- 4x y(x) - 12x y(x))log(y(x) + 3) +--R +--R + +--R 2 3 2 +--R (8x y(x) + 24x y(x))log(y(x)) + (- 12x + 36x)y(x) +--R + +--R 3 +--R (- 36x + 108x)y(x) +--R * +--R log(y(x) + 3) +--R + +--R 2 2 +--R (- 4x y(x) - 12x y(x))log(y(x)) +--R + +--R 3 2 3 +--R ((12x - 36x)y(x) + (36x - 108x)y(x))log(y(x)) +--R + +--R 5 3 2 5 3 +--R (- 9x + 54x - 36x)y(x) + (- 27x + 162x - 108x)y(x) +--R / +--R 2 +--R 36y(x) + 108y(x) +--R Type: Expression Integer +--E 86 + +--S 87 of 134 +ode30 := D(y(x),x) + x**(-a-1)*y(x)**2 - x**a +--R +--R +--R , a 2 - a - 1 +--R (85) y (x) - x + y(x) x +--R +--R Type: Expression Integer +--E 87 + +--S 88 of 134 +ode30a:=solve(ode30,y,x) +--R +--R +--R (86) "failed" +--R Type: Union("failed",...) +--E 88 + +--S 89 of 134 +ode31 := D(y(x),x) - a*x**n*(y(x)**2+1) +--R +--R +--R , 2 n +--R (87) y (x) + (- a y(x) - a)x +--R +--R Type: Expression Integer +--E 89 + +--S 90 of 134 +yx:=solve(ode31,y,x) +--R +--R +--R n log(x) +--R - a x %e + (n + 1)atan(y(x)) +--R (88) ------------------------------------ +--R n + 1 +--R Type: Union(Expression Integer,...) +--E 90 + +--S 91 of 134 +ode31expr := D(yx,x) - a*x**n*(yx**2+1) +--R +--R (89) +--R 2 , 3 2 2 3 2 n n log(x) 2 +--R (n + 2n + 1)y (x) + (- a x y(x) - a x )x (%e ) +--R +--R + +--R 2 2 2 2 2 n +--R ((2a n + 2a )x y(x) + (2a n + 2a )x)x atan(y(x)) +--R + +--R 2 2 2 +--R (- a n - 2a n - a)y(x) - a n - 2a n - a +--R * +--R n log(x) +--R %e +--R + +--R 2 2 2 n 2 +--R ((- a n - 2a n - a)y(x) - a n - 2a n - a)x atan(y(x)) +--R + +--R 2 2 2 n +--R ((- a n - 2a n - a)y(x) - a n - 2a n - a)x +--R / +--R 2 2 2 +--R (n + 2n + 1)y(x) + n + 2n + 1 +--R Type: Expression Integer +--E 91 + +--S 92 of 134 +ode32 := D(y(x),x) + y(x)**2*sin(x) - 2*sin(x)/cos(x)**2 +--R +--R +--R 2 , 2 2 +--R cos(x) y (x) + (y(x) cos(x) - 2)sin(x) +--R +--R (90) --------------------------------------- +--R 2 +--R cos(x) +--R Type: Expression Integer +--E 92 + +--S 93 of 134 +yx:=solve(ode32,y,x) +--R +--R +--R (91) "failed" +--R Type: Union("failed",...) +--E 93 + +--S 94 of 134 +ode33 := D(y(x),x) - y(x)**2*D(f(x),x)/g(x) + D(g(x),x)/f(x) +--R +--R , , 2 , +--R f(x)g(x)y (x) + g(x)g (x) - f(x)y(x) f (x) +--R +--R (92) ------------------------------------------ +--R f(x)g(x) +--R Type: Expression Integer +--E 94 + +--S 95 of 134 +ode33a:=solve(ode33,y,x) +--R +--R (93) "failed" +--R Type: Union("failed",...) +--E 95 + +--S 96 of 134 +ode34 := D(y(x),x) + f(x)*y(x)**2 + g(x)*y(x) +--R +--R , 2 +--R (94) y (x) + f(x)y(x) + g(x)y(x) +--R +--R Type: Expression Integer +--E 96 + +--S 97 of 134 +ode34a:=solve(ode34,y,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 97 + +--S 98 of 134 +ode35 := D(y(x),x) + f(x)*(y(x)**2 + 2*a*y(x) +b) +--R +--R , 2 +--R (95) y (x) + f(x)y(x) + 2a f(x)y(x) + b f(x) +--R +--R Type: Expression Integer +--E 98 + +--S 99 of 134 +yx:=solve(ode35,y,x) +--R +--R (96) +--R +--------+ x +--R | 2 ++ +--I 2\|- b + a | f(%H)d%H +--R ++ +--R + +--R +--------+ +--R 2 2 | 2 2 3 +--R (y(x) + 2a y(x) - b + 2a )\|- b + a + (2b - 2a )y(x) + 2a b - 2a +--R log(--------------------------------------------------------------------) +--R 2 +--R y(x) + 2a y(x) + b +--R / +--R +--------+ +--R | 2 +--R 2\|- b + a +--R Type: Union(Expression Integer,...) +--E 99 + +--S 100 of 134 +ode35expr := D(yx,x) + f(x)*(yx**2 + 2*a*yx +b) +--R +--R (97) +--R 2 2 3 2 2 +--R ((4b - 4a )f(x)y(x) + (8a b - 8a )f(x)y(x) + (4b - 4a b)f(x)) +--R * +--R +--------+ x 2 +--R | 2 ++ +--I \|- b + a | f(%H)d%H +--R ++ +--R + +--R 2 2 3 2 2 +--R ((4b - 4a )f(x)y(x) + (8a b - 8a )f(x)y(x) + (4b - 4a b)f(x)) +--R * +--R log +--R +--------+ +--R 2 2 | 2 2 +--R (y(x) + 2a y(x) - b + 2a )\|- b + a + (2b - 2a )y(x) +--R + +--R 3 +--R 2a b - 2a +--R / +--R 2 +--R y(x) + 2a y(x) + b +--R + +--R 3 2 2 4 +--R (8a b - 8a )f(x)y(x) + (16a b - 16a )f(x)y(x) +--R + +--R 2 3 +--R (8a b - 8a b)f(x) +--R * +--R +--------+ +--R | 2 +--R \|- b + a +--R * +--R x +--R ++ +--I | f(%H)d%H +--R ++ +--R + +--R +--------+ +--R 2 | 2 , +--R (4b - 4a )\|- b + a y (x) +--R +--R + +--R +--------+ +--R 2 | 2 +--R (- f(x)y(x) - 2a f(x)y(x) - b f(x))\|- b + a +--R * +--R log +--R +--------+ +--R 2 2 | 2 2 +--R (y(x) + 2a y(x) - b + 2a )\|- b + a + (2b - 2a )y(x) + 2a b +--R + +--R 3 +--R - 2a +--R / +--R 2 +--R y(x) + 2a y(x) + b +--R ** +--R 2 +--R + +--R 3 2 2 4 2 3 +--R ((4a b - 4a )f(x)y(x) + (8a b - 8a )f(x)y(x) + (4a b - 4a b)f(x)) +--R * +--R +--------+ +--R 2 2 | 2 2 3 +--R (y(x) + 2a y(x) - b + 2a )\|- b + a + (2b - 2a )y(x) + 2a b - 2a +--R log(--------------------------------------------------------------------) +--R 2 +--R y(x) + 2a y(x) + b +--R + +--R 2 2 2 2 +--R (4b + (- 4a + 4)b - 4a )f(x)y(x) +--R + +--R 2 3 3 +--R (8a b + (- 8a + 8a)b - 8a )f(x)y(x) +--R + +--R 3 2 2 2 +--R (4b + (- 4a + 4)b - 4a b)f(x) +--R * +--R +--------+ +--R | 2 +--R \|- b + a +--R / +--R +--------+ +--R 2 2 3 2 2 | 2 +--R ((4b - 4a )y(x) + (8a b - 8a )y(x) + 4b - 4a b)\|- b + a +--R Type: Expression Integer +--E 100 + +--S 101 of 134 +ode36 := D(y(x),x) + y(x)**3 + a*x*y(x)**2 +--R +--R +--R , 3 2 +--R (98) y (x) + y(x) + a x y(x) +--R +--R Type: Expression Integer +--E 101 + +--S 102 of 134 +ode36a:=solve(ode36,y,x) +--R +--R +--R (99) "failed" +--R Type: Union("failed",...) +--E 102 + +--S 103 of 134 +ode37 := D(y(x),x) - y(x)**3 - a*exp(x)*y(x)**2 +--R +--R , 2 x 3 +--R (100) y (x) - a y(x) %e - y(x) +--R +--R Type: Expression Integer +--E 103 + +--S 104 of 134 +ode37a:=solve(ode37,y,x) +--R +--R (101) "failed" +--R Type: Union("failed",...) +--E 104 + +--S 105 of 134 +ode38 := D(y(x),x) - a*y(x)**3 - b*x**(3/2) +--R +--R , +-+ 3 +--R (102) y (x) - b x\|x - a y(x) +--R +--R Type: Expression Integer +--E 105 + +--S 106 of 134 +ode38a:=solve(ode38,y,x) +--R +--R (103) "failed" +--R Type: Union("failed",...) +--E 106 + +--S 107 of 134 +ode39 := D(y(x),x) - a3*y(x)**3 - a2*y(x)**2 - a1*y(x) - a0 +--R +--R , 3 2 +--R (104) y (x) - a3 y(x) - a2 y(x) - a1 y(x) - a0 +--R +--R Type: Expression Integer +--E 107 + +--S 108 of 134 +yx:=solve(ode39,y,x) +--R +--R +--R (105) +--R ROOT +--R 2 2 3 3 2 2 +--R (- 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2 + 3a1 a2 ) +--R * +--R 2 +--I %%CK0 +--R + +--R 2 +--R 12a1 a3 - 4a2 +--R / +--R 2 2 3 3 2 2 +--R 27a0 a3 + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2 - a1 a2 +--R + +--I - %%CK0 +--R * +--R log +--R 2 3 2 2 2 4 2 +--R 162a0 a1 a3 + (- 54a0 a2 - 108a0 a1 a2 + 24a1 )a3 +--R + +--R 3 3 2 5 2 4 +--R (60a0 a1 a2 - 14a1 a2 )a3 - 8a0 a2 + 2a1 a2 +--R * +--I %%CK0 +--R + +--R 2 3 3 2 3 2 2 +--R 81a0 a3 + (- 54a0 a1 a2 + 12a1 )a3 + (12a0 a2 - 3a1 a2 )a3 +--R * +--R ROOT +--R 2 2 3 3 +--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2 +--R + +--R 2 2 +--R 3a1 a2 +--R * +--R 2 +--I %%CK0 +--R + +--R 2 +--R 12a1 a3 - 4a2 +--R / +--R 2 2 3 3 2 2 +--R 27a0 a3 + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2 - a1 a2 +--R + +--R 2 3 2 2 2 4 2 +--R 162a0 a1 a3 + (- 54a0 a2 - 108a0 a1 a2 + 24a1 )a3 +--R + +--R 3 3 2 5 2 4 +--R (60a0 a1 a2 - 14a1 a2 )a3 - 8a0 a2 + 2a1 a2 +--R * +--R 2 +--I %%CK0 +--R + +--R 2 3 3 2 +--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 +--R + +--R 3 2 2 +--R (- 12a0 a2 + 3a1 a2 )a3 +--R * +--I %%CK0 +--R + +--R 3 2 3 2 2 +--R (54a0 a3 - 18a1 a2 a3 + 4a2 a3)y(x) + (18a0 a2 - 12a1 )a3 +--R + +--R 2 +--R 2a1 a2 a3 +--R + +--R - +--R ROOT +--R 2 2 3 3 +--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2 +--R + +--R 2 2 +--R 3a1 a2 +--R * +--R 2 +--I %%CK0 +--R + +--R 2 +--R 12a1 a3 - 4a2 +--R / +--R 2 2 3 3 2 2 +--R 27a0 a3 + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2 - a1 a2 +--R + +--I - %%CK0 +--R * +--R log +--R 2 3 2 2 2 4 2 +--R - 162a0 a1 a3 + (54a0 a2 + 108a0 a1 a2 - 24a1 )a3 +--R + +--R 3 3 2 5 2 4 +--R (- 60a0 a1 a2 + 14a1 a2 )a3 + 8a0 a2 - 2a1 a2 +--R * +--I %%CK0 +--R + +--R 2 3 3 2 3 2 2 +--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 + (- 12a0 a2 + 3a1 a2 )a3 +--R * +--R ROOT +--R 2 2 3 3 +--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 - 12a0 a2 +--R + +--R 2 2 +--R 3a1 a2 +--R * +--R 2 +--I %%CK0 +--R + +--R 2 +--R 12a1 a3 - 4a2 +--R / +--R 2 2 3 3 2 2 +--R 27a0 a3 + (- 18a0 a1 a2 + 4a1 )a3 + 4a0 a2 - a1 a2 +--R + +--R 2 3 2 2 2 4 2 +--R 162a0 a1 a3 + (- 54a0 a2 - 108a0 a1 a2 + 24a1 )a3 +--R + +--R 3 3 2 5 2 4 +--R (60a0 a1 a2 - 14a1 a2 )a3 - 8a0 a2 + 2a1 a2 +--R * +--R 2 +--I %%CK0 +--R + +--R 2 3 3 2 +--R - 81a0 a3 + (54a0 a1 a2 - 12a1 )a3 +--R + +--R 3 2 2 +--R (- 12a0 a2 + 3a1 a2 )a3 +--R * +--I %%CK0 +--R + +--R 3 2 3 2 2 +--R (54a0 a3 - 18a1 a2 a3 + 4a2 a3)y(x) + (18a0 a2 - 12a1 )a3 +--R + +--R 2 +--R 2a1 a2 a3 +--R + +--I 2%%CK0 +--R * +--R log +--R 2 3 2 2 2 4 2 +--R - 162a0 a1 a3 + (54a0 a2 + 108a0 a1 a2 - 24a1 )a3 +--R + +--R 3 3 2 5 2 4 +--R (- 60a0 a1 a2 + 14a1 a2 )a3 + 8a0 a2 - 2a1 a2 +--R * +--R 2 +--I %%CK0 +--R + +--R 2 3 3 2 3 2 2 +--R (81a0 a3 + (- 54a0 a1 a2 + 12a1 )a3 + (12a0 a2 - 3a1 a2 )a3) +--R * +--I %%CK0 +--R + +--R 3 2 3 2 2 +--R (27a0 a3 - 9a1 a2 a3 + 2a2 a3)y(x) + (9a0 a2 + 12a1 )a3 +--R + +--R 2 4 +--R - 11a1 a2 a3 + 2a2 +--R + +--R - 2x +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 108 + +--S 109 of 134 +ode40 := D(y(x),x) + 3*a*y(x)**3 + 6*a*x*y(x)**2 +--R +--R , 3 2 +--R (106) y (x) + 3a y(x) + 6a x y(x) +--R +--R Type: Expression Integer +--E 109 + +--S 110 of 134 +ode40a:=solve(ode40,y,x) +--R +--R (107) "failed" +--R Type: Union("failed",...) +--E 110 + +--S 111 of 134 +ode41 := D(y(x),x) + a*x*y(x)**3 + b*y(x)**2 +--R +--R , 3 2 +--R (108) y (x) + a x y(x) + b y(x) +--R +--R Type: Expression Integer +--E 111 + +--S 112 of 134 +ode41a:=solve(ode41,y,x) +--R +--R (109) "failed" +--R Type: Union("failed",...) +--E 112 + +--S 113 of 134 +ode42 := D(y(x),x) - x*(x+2)*y(x)**3 - (x+3)*y(x)**2 +--R +--R , 2 3 2 +--R (110) y (x) + (- x - 2x)y(x) + (- x - 3)y(x) +--R +--R Type: Expression Integer +--E 113 + +--S 114 of 134 +ode42a:=solve(ode42,y,x) +--R +--R (111) "failed" +--R Type: Union("failed",...) +--E 114 + +--S 115 of 134 +ode43 := D(y(x),x) + (3*a*x**2 + 4*a**2*x + b)*y(x)**3 + 3*x*y(x)**2 +--R +--R , 2 2 3 2 +--R (112) y (x) + (3a x + 4a x + b)y(x) + 3x y(x) +--R +--R Type: Expression Integer +--E 115 + +--S 116 of 134 +ode43a:=solve(ode43,y,x) +--R +--R (113) "failed" +--R Type: Union("failed",...) +--E 116 + +--S 117 of 134 +ode44 := D(y(x),x) + 2*a*x**3*y(x)**3 + 2*x*y(x) +--R +--R , 3 3 +--R (114) y (x) + 2a x y(x) + 2x y(x) +--R +--R Type: Expression Integer +--E 117 + +--S 118 of 134 +yx:=solve(ode44,y,x) +--R +--R 2 2 +--R (2a x + a)y(x) + 2 +--R (115) -------------------- +--R 2 +--R 2 2x +--R 2y(x) %e +--R Type: Union(Expression Integer,...) +--E 118 + +--S 119 of 134 +ode44expr := D(yx,x) + 2*a*x**3*yx**3 + 2*x*yx +--R +--R (116) +--R 2 2 2 2 +--R 3 2x , 3 6 4 2x +--R - 8y(x) (%e ) y (x) + ((- 8a x + 4a x)y(x) - 8x y(x) )(%e ) +--R +--R + +--R 4 9 4 7 4 5 4 3 6 3 7 3 5 3 3 4 +--R (8a x + 12a x + 6a x + a x )y(x) + (24a x + 24a x + 6a x )y(x) +--R + +--R 2 5 2 3 2 3 +--R (24a x + 12a x )y(x) + 8a x +--R / +--R 2 3 +--R 6 2x +--R 4y(x) (%e ) +--R Type: Expression Integer +--E 119 + +--S 120 of 134 +ode45 := D(y(x),x) + 2*(a**2*x**3 - b**2*x)*y(x)**3 + 3*b*y(x)**2 +--R +--R , 2 3 2 3 2 +--R (117) y (x) + (2a x - 2b x)y(x) + 3b y(x) +--R +--R Type: Expression Integer +--E 120 + +--S 121 of 134 +ode45a:=solve(ode45,y,x) +--R +--R (118) "failed" +--R Type: Union("failed",...) +--E 121 + +--S 122 of 134 +ode46 := D(y(x),x) - x**a*y(x)**3 + 3*y(x)**2 - x**(-a)*y(x) _ + -x**(-2*a) + a*x**(-a-1) +--R +--R , 3 a - a - a - 1 - 2a 2 +--R (119) y (x) - y(x) x - y(x)x + a x - x + 3y(x) +--R +--R Type: Expression Integer +--E 122 + +--S 123 of 134 +ode46a:=solve(ode46,y,x) +--R +--R (120) "failed" +--R Type: Union("failed",...) +--E 123 + +--S 124 of 134 +ode47 := D(y(x),x) - a*(x**n - x)*y(x)**3 - y(x)**2 +--R +--R , 3 n 3 2 +--R (121) y (x) - a y(x) x + a x y(x) - y(x) +--R +--R Type: Expression Integer +--E 124 + +--S 125 of 134 +ode47a:=solve(ode47,y,x) +--R +--R (122) "failed" +--R Type: Union("failed",...) +--E 125 + +--S 126 of 134 +ode48 := D(y(x),x) - (a*x**n + b*x)*y(x)**3 - c*y(x)**2 +--R +--R , 3 n 3 2 +--R (123) y (x) - a y(x) x - b x y(x) - c y(x) +--R +--R Type: Expression Integer +--E 126 + +--S 127 of 134 +ode48a:=solve(ode48,y,x) +--R +--R (124) "failed" +--R Type: Union("failed",...) +--E 127 + +--S 128 of 134 +ode49 := D(y(x),x) + a*diff(phi(x),x)*y(x)**3 + 6*a*phi(x)*y(x)**2 + _ + (2*a+1)*y(x)*diff(phi(x),x,x)/diff(phi(x),x) +2*(a+1) +--R +--R There are no library operations named phi +--R Use HyperDoc Browse or issue +--R )what op phi +--R to learn if there is any operation containing " phi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named phi +--R with argument type(s) +--R Variable x +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 128 + +--S 129 of 134 +f1 := operator 'f1 +--R +--R (125) f1 +--R Type: BasicOperator +--E 129 + +--S 130 of 134 +f2 := operator 'f2 +--R +--R (126) f2 +--R Type: BasicOperator +--E 130 + +--S 131 of 134 +f3 := operator 'f3 +--R +--R (127) f3 +--R Type: BasicOperator +--E 131 + +--S 132 of 134 +f0 := operator 'f0 +--R +--R (128) f0 +--R Type: BasicOperator +--E 132 + +--S 133 of 134 +ode50 := D(y(x),x) - f3(x)*y(x)**3 - f2(x)*y(x)**2 - f1(x)*y(x) - f0(x) +--R +--R , 3 2 +--R (129) y (x) - f3(x)y(x) - f2(x)y(x) - f1(x)y(x) - f0(x) +--R +--R Type: Expression Integer +--E 133 + +--S 134 of 134 +ode50a:=solve(ode50,y,x) +--R +--R (130) "failed" +--R Type: Union("failed",...) +--E 134 + +)spool +)lisp (bye) + +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} {\bf http://www.cs.uwaterloo.ca/$\tilde{}$ecterrab/odetools.html} +\end{thebibliography} +\end{document}