diff --git a/changelog b/changelog index c90262b..667795f 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100331 tpd src/axiom-website/patches.html 20100331.01.tpd.patch +20100331 tpd src/input/zimmer.input run the zimmerman test suite +20100331 tpd src/input/Makefile add zimmer regression file 20100330 tpd src/axiom-website/patches.html 20100330.02.tpd.patch 20100330 tpd src/input/Makefile add davenport.input 20100330 tpd src/input/davenport.input examples from DST88 paper diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 9c17253..0189d71 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2597,5 +2597,7 @@ src/axiom-website/download.html add march 2010 ubuntu
src/axiom-website/download.html change 2009 -> 2010 on new links
20100330.02.tpd.patch src/input/davenport.input examples from DST88 paper
+20100331.01.tpd.patch +src/input/zimmer.input run the zimmerman test suite
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 67cf307..bcacc33 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -240,8 +240,7 @@ SKIP= as-eg1.output as-eg2.output \ s21bcf.output s21bdf.output saddle.output \ sininv.output sinsin2.output sinsin.output spiral.output \ tetra.output tknot.output tschirn.output typo.output \ - vectors.output wester.output wiggle.output zimmbron.output \ - zimmer.output + vectors.output wester.output wiggle.output zimmbron.output # Error ASEC is invalid as a function. ASEC=errortrap.output @@ -275,7 +274,7 @@ OUTS= ffrac.output \ vector.output viewdef.output \ wutset.output \ xpoly.output xpr.output \ - zdsolve.output zimmer.output zlindep.output + zdsolve.output zlindep.output REGRES= ackermann.regress \ algaggr.regress algbrbf.regress algfacob.regress alist.regress \ @@ -400,7 +399,7 @@ REGRES= ackermann.regress \ triglim.regress tsetcatvermeer.regress tutchap1.regress \ typetower.regress void.regress uniseg.regress \ unittest1.regress unittest2.regress unittest3.regress unittest4.regress \ - unit-i-funsel.regress unit-macro.regress zimmbron.regress + unit-i-funsel.regress unit-macro.regress zimmbron.regress zimmer.regress IN= ${SRC}/input MID= ${INT}/input diff --git a/src/input/zimmer.input.pamphlet b/src/input/zimmer.input.pamphlet index bf5a824..efc88fe 100644 --- a/src/input/zimmer.input.pamphlet +++ b/src/input/zimmer.input.pamphlet @@ -2,7 +2,7 @@ \usepackage{axiom} \begin{document} \title{\$SPAD/src/input zimmer.input} -\author{The Axiom Team} +\author{Timothy Daly} \maketitle \begin{abstract} These examples come from Postel and Zimmermann's paper in the 5th Rhine @@ -11,379 +11,1899 @@ Conference on Computer Algebra. \eject \tableofcontents \eject -\section{License} -\begin{chunk}{license} ---Copyright The Numerical Algorithms Group Limited 1996. -\end{chunk} \begin{chunk}{*} -\getchunk{license} )set break resume +)sys rm -f zimmer.output +)spool zimmer.output +)set message test on +)set message auto off -- First Order Equations --- 1 - +--S 1 of 177 u := operator 'u +--R +--R +--R (1) u +--R Type: BasicOperator +--E 1 + +--S 2 of 177 ode := (x^4-x^3)*D(u x,x) + 2*x^4*u(x) = x^3/3 + C +--R +--R +--R 3 +--R 4 3 , 4 x + 3C +--R (2) (x - x )u (x) + 2x u(x)= ------- +--R 3 +--R Type: Equation Expression Integer +--E 2 + +--S 3 of 177 solve(ode,u,x) +--R +--R +--R 3 2 - 2x +--R 2x - 3x + 6C %e +--R (3) [particular= ------------------,basis= [-----------]] +--R 4 3 2 2 +--R 12x - 24x + 12x x - 2x + 1 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 3 --- 2 )clear all + +--S 4 of 177 u := operator 'u +--R +--R +--R (1) u +--R Type: BasicOperator +--E 4 + +--S 5 of 177 ode := -D(u x,x)/2 + u(x) = sin(x) +--R +--R +--R , +--R - u (x) + 2u(x) +--R +--R (2) ---------------= sin(x) +--R 2 +--R Type: Equation Expression Integer +--E 5 + +--S 6 of 177 solve(ode,u,x) +--R +--R +--R 4sin(x) + 2cos(x) 2x +--R (3) [particular= -----------------,basis= [%e ]] +--R 5 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 6 --- 3 )clear all + +--S 7 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 7 + +--S 8 of 177 ode := D(y x,x) = y(x)/(y(x)*log(y(x)) + x) +--R +--R +--R , y(x) +--R (2) y (x)= ----------------- +--R y(x)log(y(x)) + x +--R Type: Equation Expression Integer +--E 8 + +--S 9 of 177 solve(ode,y,x) +--R +--R +--R 2 +--R y(x)log(y(x)) - 2x +--R (3) ------------------- +--R 2y(x) +--R Type: Union(Expression Integer,...) +--E 9 --- 4 )clear all + +--S 10 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 10 + +--S 11 of 177 ode := 2*y(x)*D(y x,x)^2 -2*x*D(y x,x)-y(x) = 0 +--R +--R +--R , 2 , +--R (2) 2y(x)y (x) - 2xy (x) - y(x)= 0 +--R +--R Type: Equation Expression Integer +--E 11 + +--S 12 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R getlincoeff: not an appropriate ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 12 --- 5 )clear all + +--S 13 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 13 + +--S 14 of 177 ode := D(y x,x) + y(x) = y(x)^3*sin(x) +--R +--R +--R , 3 +--R (2) y (x) + y(x)= y(x) sin(x) +--R +--R Type: Equation Expression Integer +--E 14 + +--S 15 of 177 solve(ode,y,x) +--R +--R +--R 2 2 +--R - 4y(x) sin(x) - 2y(x) cos(x) + 5 +--R (3) --------------------------------- +--R 2 2x +--R 5y(x) %e +--R Type: Union(Expression Integer,...) +--E 15 --- 6 )clear all + +--S 16 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 16 + +--S 17 of 177 P := operator 'P +--R +--R +--R (2) P +--R Type: BasicOperator +--E 17 + +--S 18 of 177 Q := operator 'Q +--R +--R +--R (3) Q +--R Type: BasicOperator +--E 18 + +--S 19 of 177 ode := D(y x,x) + P(x)*y(x) = Q(x)*y(x)^n +--R +--R +--R , n +--R (4) y (x) + P(x)y(x)= Q(x)y(x) +--R +--R Type: Equation Expression Integer +--E 19 + +--S 20 of 177 solve(ode,y,x) +--R +--R +--R (5) "failed" +--R Type: Union("failed",...) +--E 20 + +--S 21 of 177 solve(eval(ode,n=1),y,x) +--R +--R +--R x +--R ++ +--I | (Q(%J) - P(%J))d%J +--R ++ +--R (6) [particular= 0,basis= [%e ]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 21 + +--S 22 of 177 solve(eval(ode,n=2),y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 22 + +--S 23 of 177 solve(eval(ode,n=%pi),y,x) +--R +--R +--R (7) "failed" +--R Type: Union("failed",...) +--E 23 + +--S 24 of 177 solve(eval(ode,n=%e),y,x) +--R +--R +--R (8) "failed" +--R Type: Union("failed",...) +--E 24 + +--S 25 of 177 solve(eval(ode,n=sqrt(2)),y,x) +--R +--R +--R (9) "failed" +--R Type: Union("failed",...) +--E 25 --- 7 )clear all + +--S 26 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 26 + +--S 27 of 177 ode := (x^2-1)*D(y x,x)^2 - 2*x*y(x)*D(y x,x)+(y x)^2 - 1 = 0 +--R +--R +--R 2 , 2 , 2 +--R (2) (x - 1)y (x) - 2x y(x)y (x) + y(x) - 1= 0 +--R +--R Type: Equation Expression Integer +--E 27 + +--S 28 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R getlincoeff: not an appropriate ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 28 --- 8 )clear all + +--S 29 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 29 + +--S 30 of 177 f := operator 'f +--R +--R +--R (2) f +--R Type: BasicOperator +--E 30 + +--S 31 of 177 g := operator 'g +--R +--R +--R (3) g +--R Type: BasicOperator +--E 31 + +--S 32 of 177 ode := f(x*D(y x,x) - y(x)) = g(D(y x,x)) +--R +--R +--R , , +--R (4) f(xy (x) - y(x))= g(y (x)) +--R +--R Type: Equation Expression Integer +--E 32 + +--S 33 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R parseODE: equation has order 0 +--R +--R Continuing to read the file... +--R +--E 33 --- 9 )clear all + +--S 34 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 34 + +--S 35 of 177 ode := D(y x,x) = (3*x^2-y(x)^2-7)/(exp(y(x))+2*x*y(x)+1) +--R +--R +--R 2 2 +--R , - y(x) + 3x - 7 +--R (2) y (x)= -------------------- +--R y(x) +--R %e + 2x y(x) + 1 +--R Type: Equation Expression Integer +--E 35 + +--S 36 of 177 solve(ode,y,x) +--R +--R +--R y(x) 2 3 +--R (3) %e + x y(x) + y(x) - x + 7x +--R Type: Union(Expression Integer,...) +--E 36 --- 10 )clear all + +--S 37 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 37 + +--S 38 of 177 ode := D(y x,x) = (2*x^3*y(x) - (y x)^4)/(x^4 - 2*x*(y x)^3) +--R +--R +--R 4 3 +--R , y(x) - 2x y(x) +--R (2) y (x)= --------------- +--R 3 4 +--R 2x y(x) - x +--R Type: Equation Expression Integer +--E 38 + +--S 39 of 177 solve(ode,y,x) +--R +--R +--R (3) "failed" +--R Type: Union("failed",...) +--E 39 --- 11 )clear all + +--S 40 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 40 + +--S 41 of 177 ode := D(y x,x)*(D(y x,x) + y(x)) = x*(x + y(x)) +--R +--R +--R , 2 , 2 +--R (2) y (x) + y(x)y (x)= x y(x) + x +--R +--R Type: Equation Expression Integer +--E 41 + +--S 42 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R getlincoeff: not an appropriate ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 42 --- 12 )clear all + +--S 43 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 43 + +--S 44 of 177 ode := D(y x,x) = x/(x^2*(y x)^2 + (y x)^5) +--R +--R +--R , x +--R (2) y (x)= --------------- +--R 5 2 2 +--R y(x) + x y(x) +--R Type: Equation Expression Integer +--E 44 + +--S 45 of 177 solve(ode,y,x) +--R +--R +--R 3 +--R 2y(x) +--R - ------ +--R 3 2 3 +--R (- 2y(x) - 2x - 3)%e +--R (3) ------------------------------ +--R 4 +--R Type: Union(Expression Integer,...) +--E 45 --- 13 )clear all + +--S 46 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 46 + +--S 47 of 177 ode := y(x) = 2*x*D(y x,x) - a*D(y x,x)^3 +--R +--R +--R , 3 , +--R (2) y(x)= - a y (x) + 2xy (x) +--R +--R Type: Equation Expression Integer +--E 47 + +--S 48 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R getlincoeff: not an appropriate ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 48 --- 14 )clear all + +--S 49 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 49 + +--S 50 of 177 ode := y(x) = 2*x*D(y x,x) - D(y x,x)^3 +--R +--R +--R , 3 , +--R (2) y(x)= - y (x) + 2xy (x) +--R +--R Type: Equation Expression Integer +--E 50 + +--S 51 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R getlincoeff: not an appropriate ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 51 --- 15 )clear all + +--S 52 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 52 + +--S 53 of 177 ode := D(y x,x) = exp(x)*(y x)^2 - y(x) + exp(-x) +--R +--R +--R , 2 x - x +--R (2) y (x)= y(x) %e + %e - y(x) +--R +--R Type: Equation Expression Integer +--E 53 + +--S 54 of 177 solve(ode,y,x) +--R +--R +--R (3) "failed" +--R Type: Union("failed",...) +--E 54 --- 16 )clear all + +--S 55 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 55 + +--S 56 of 177 ode := D(y x,x) = (y x)^2 - x*y(x) + 1 +--R +--R +--R , 2 +--R (2) y (x)= y(x) - x y(x) + 1 +--R +--R Type: Equation Expression Integer +--E 56 + +--S 57 of 177 solve(ode,y,x) +--R +--R +--R 2 +--R x +--R - -- x +--R 2 ++ 1 +--I (- y(x) + x)%e | - ------- d%J + 1 +--R ++ 2 +--I %J +--R - --- +--R 2 +--R %e +--R (3) ----------------------------------------- +--R 2 +--R x +--R - -- +--R 2 +--R (y(x) - x)%e +--R Type: Union(Expression Integer,...) +--E 57 --- 17 )clear all + +--S 58 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 58 + +--S 59 of 177 ode := D(y x,x) = (9*x^8 + 1)/((y x)^2 +1) +--R +--R +--R 8 +--R , 9x + 1 +--R (2) y (x)= --------- +--R 2 +--R y(x) + 1 +--R Type: Equation Expression Integer +--E 59 + +--S 60 of 177 solve(ode,y,x) +--R +--R +--R 3 9 +--R y(x) + 3y(x) - 3x - 3x +--R (3) ------------------------ +--R 3 +--R Type: Union(Expression Integer,...) +--E 60 --- 18 )clear all + +--S 61 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 61 + +--S 62 of 177 ode := y(x)=2*x*D(y x,x) + y(x)*D(y x,x)^2 +--R +--R +--R , 2 , +--R (2) y(x)= y(x)y (x) + 2xy (x) +--R +--R Type: Equation Expression Integer +--E 62 + +--S 63 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R getlincoeff: not an appropriate ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 63 --- 19 )clear all + + +--S 64 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 64 + +--S 65 of 177 ode := x = y(x)*D(y x,x) - x*D(y x,x)^2 +--R +--R +--R , 2 , +--R (2) x= - x y (x) + y(x)y (x) +--R +--R Type: Equation Expression Integer +--E 65 + +--S 66 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R getlincoeff: not an appropriate ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 66 -- Second Order Equations --- 20 )clear all + +--S 67 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 67 + +--S 68 of 177 ode := D(y x,x,2)*(a*x+b)^2+4*D(y x,x)*(a*x+b)*a+2*y(x)*a^2=0 +--R +--R +--R 2 2 2 ,, 2 , 2 +--R (2) (a x + 2a b x + b )y (x) + (4a x + 4a b)y (x) + 2a y(x)= 0 +--R +--R Type: Equation Expression Integer +--E 68 + +--S 69 of 177 solve(ode,y,x) +--R +--R +--R x 2a x + b +--R (3) [particular= 0,basis= [------------------,------------------]] +--R 2 2 2 2 2 2 +--R a x + 2a b x + b a x + 2a b x + b +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 69 --- 21 )clear all + +--S 70 of 177 u := operator 'u +--R +--R +--R (1) u +--R Type: BasicOperator +--E 70 + +--S 71 of 177 ode := (x^2 - x)*D(u x,x,2) + (2*x^2+4*x-3)*D(u x,x) + 8*x*u(x)=1 +--R +--R +--R 2 ,, 2 , +--R (2) (x - x)u (x) + (2x + 4x - 3)u (x) + 8x u(x)= 1 +--R +--R Type: Equation Expression Integer +--E 71 + +--S 72 of 177 solve(ode,u,x) +--R +--R +--R 3 2 - 2x +--R 2x - 3x + 53 1 %e +--R (3) [particular= ------------------,basis= [-------------,-----------]] +--R 4 3 2 4 3 2 2 +--R 12x - 24x + 12x x - 2x + x x - 2x + 1 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 72 --- 22 )clear all + +--S 73 of 177 w := operator 'w +--R +--R +--R (1) w +--R Type: BasicOperator +--E 73 + +--S 74 of 177 ode := (x^2 - x)*D(w x,x,2) + (1-2*x^2)*D(w x,x) + (4*x - 2)*w(x) = 0 +--R +--R +--R 2 ,, 2 , +--R (2) (x - x)w (x) + (- 2x + 1)w (x) + (4x - 2)w(x)= 0 +--R +--R Type: Equation Expression Integer +--E 74 + +--S 75 of 177 solve(ode,w,x) +--R +--R +--R 2 2x +--R (3) [particular= 0,basis= [x ,%e ]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 75 --- 23 -)clear all +)clear all + +--S 76 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 76 + +--S 77 of 177 ode := D(y x,x,2) - D(y x,x) = 2*y(x)*D(y x,x) +--R +--R +--R ,, , , +--R (2) y (x) - y (x)= 2y(x)y (x) +--R +--R Type: Equation Expression Integer +--E 77 + +--S 78 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R getfreelincoeff: not a linear ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 78 --- 24 )clear all + +--S 79 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 79 + +--S 80 of 177 ode := D(y x,x,2)/y(x) - D(y x,x)^2/y(x)^2 -1 + y(x)^(-3) = 0 +--R +--R +--R 2 ,, , 2 3 +--R y(x) y (x) - y(x)y (x) - y(x) + 1 +--R +--R (2) ------------------------------------= 0 +--R 3 +--R y(x) +--R Type: Equation Expression Integer +--E 80 + +--S 81 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R parseLODE: not a linear ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 81 --- 25 )clear all + + +--S 82 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 82 + +--S 83 of 177 ode := D(y x,x,2) + 2*x*D(y x,x) = 2*x +--R +--R +--R ,, , +--R (2) y (x) + 2xy (x)= 2x +--R +--R Type: Equation Expression Integer +--E 83 + +--S 84 of 177 solve(ode,y,x) +--R +--R +--R (3) [particular= x,basis= [1,erf(x)]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 84 --- 26 )clear all + +--S 85 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 85 + +--S 86 of 177 ode := 2*y(x)*D(y x,x,2) - D(y x,x)^2 = (D(y x,x) - x*D(y x,x,2))^2/3 +--R +--R +--R 2 ,, 2 , ,, , 2 +--R x y (x) - 2xy (x)y (x) + y (x) +--R ,, , 2 +--R (2) 2y(x)y (x) - y (x) = ---------------------------------- +--R 3 +--R Type: Equation Expression Integer +--E 86 + +--S 87 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R getlincoeff: not an appropriate ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 87 --- 27 )clear all + + +--S 88 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 88 + +--S 89 of 177 ode := x*D(y x,x,2) = 2*y(x)*D(y x,x) +--R +--R +--R ,, , +--R (2) xy (x)= 2y(x)y (x) +--R +--R Type: Equation Expression Integer +--E 89 + +--S 90 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R getfreelincoeff: not a linear ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 90 --- 28 )clear all + + +--S 91 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 91 + +--S 92 of 177 ode := (1-x)*(y(x)*D(y x,x,2) - D(y x,x)^2) + x^2*y(x)^2 = 0 +--R +--R +--R ,, , 2 2 2 +--R (2) (- x + 1)y(x)y (x) + (x - 1)y (x) + x y(x) = 0 +--R +--R Type: Equation Expression Integer +--E 92 + +--S 93 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R parseLODE: not a linear ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 93 --- 29 )clear all + +--S 94 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 94 + +--S 95 of 177 ode := x*y(x)*D(y x,x,2) + x*D(y x,x)^2 + y(x)*D(y x,x) = 0 +--R +--R +--R ,, , 2 , +--R (2) x y(x)y (x) + x y (x) + y(x)y (x)= 0 +--R +--R Type: Equation Expression Integer +--E 95 + +--S 96 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R parseLODE: not a linear ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 96 --- 30 )clear all + +--S 97 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 97 + +--S 98 of 177 ode := D(y x,x,2)^2 - 2*D(y x,x,2)*D(y x,x) + 2*y(x)*D(y x,x) -y(x)^2 = 0 +--R +--R +--R ,, 2 , ,, , 2 +--R (2) y (x) - 2y (x)y (x) + 2y(x)y (x) - y(x) = 0 +--R +--R Type: Equation Expression Integer +--E 98 + +--S 99 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R getlincoeff: not an appropriate ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 99 --- 31 )clear all + +--S 100 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 100 + +--S 101 of 177 ode := (x^3/2-x^2)*D(y x,x,2) + (2*x^2-3*x+1)*D(y x,x) + (x-1)*y(x) = 0 +--R +--R +--R 3 2 ,, 2 , +--R (x - 2x )y (x) + (4x - 6x + 2)y (x) + (2x - 2)y(x) +--R +--R (2) -----------------------------------------------------= 0 +--R 2 +--R Type: Equation Expression Integer +--E 101 + +--S 102 of 177 solve(ode,y,x) +--R +--R +--R (3) +--R [particular= 0, +--R 1 1 1 +--R - - +-------+ - - +-------+ x -- +----------+ +--I x | 1 x | 1 ++ %J | 1 +--I basis= [%e |------- ,%e |------- | %e |---------- d%J ]] +--R | 2 | 2 ++ | 4 3 +--I \|x - 2x \|x - 2x \|%J - 2%J +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 102 --- 32 )clear all + +--S 103 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 103 + +--S 104 of 177 ode := D(y x,x,2) - 2*x*D(y x,x) + 2*y(x) = 3 +--R +--R +--R ,, , +--R (2) y (x) - 2xy (x) + 2y(x)= 3 +--R +--R Type: Equation Expression Integer +--E 104 + +--S 105 of 177 solve(ode,y,x) +--R +--R +--R 2 +--I x %J +--R 3 ++ %e +--I (3) [particular= -,basis= [x,x | ----- d%J ]] +--R 2 ++ 2 +--I %J +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 105 --- 33 )clear all + +--S 106 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 106 + +--S 107 of 177 ode := sqrt(x)*D(y x,x,2) + 2*x*D(y x,x) + 3*y(x) = 0 +--R +--R +--R +-+ ,, , +--R (2) \|x y (x) + 2xy (x) + 3y(x)= 0 +--R +--R Type: Equation Expression Integer +--E 107 + +--S 108 of 177 solve(ode,y,x) +--R +--R +--R (3) [particular= 0,basis= []] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 108 --- 34 )clear all + +--S 109 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 109 + +--S 110 of 177 ode := x^2*D(y x,x,2) + 3*x*D(y x,x) = 1/(x^4*y(x)^3) +--R +--R +--R 2 ,, , 1 +--R (2) x y (x) + 3xy (x)= ------- +--R 4 3 +--R x y(x) +--R Type: Equation Expression Integer +--E 110 + +--S 111 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R getlincoeff: not an appropriate ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 111 --- 35 )clear all + +--S 112 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 112 + +--S 113 of 177 ode := D(y x,x,2) - 2/x^2*y(x) = 7*x^4 +3*x^3 +--R +--R +--R 2 ,, +--R x y (x) - 2y(x) +--R 4 3 +--R (2) ----------------= 7x + 3x +--R 2 +--R x +--R Type: Equation Expression Integer +--E 113 + +--S 114 of 177 solve(ode,y,x) +--R +--R +--R 7 6 3 3 3 +--R 3x + 2x - 7x + 14 x - 1 x + 2 +--R (3) [particular= --------------------,basis= [------,------]] +--R 12x x x +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 114 --- 36 )clear all + +--S 115 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 115 + +--S 116 of 177 ode := D(y x,x,2) +y(x) = csc(x) +--R +--R +--R ,, +--R (2) y (x) + y(x)= csc(x) +--R +--R Type: Equation Expression Integer +--E 116 + +--S 117 of 177 solve(ode,y,x) +--R +--R +--R (3) +--R sin(x) 2 +--R [particular= sin(x)log(----------) - sin(x)log(----------) - x cos(x), +--R cos(x) + 1 cos(x) + 1 +--R basis= [cos(x),sin(x)]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 117 -- Higher Order Equations --- 37 )clear all + +--S 118 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 118 + +--S 119 of 177 ode := D(y x,x,7) - 14*D(y x,x,6) +80*D(y x,x,5) -242*D(y x,x,4) + _ 419*D(y x,x,3) - 416*D(y x,x,2) +220*D(y x,x) -48*y(x) = 0 +--R +--R +--R (2) +--R (vii) (vi) (v) (iv) ,,, ,, +--R y (x) - 14y (x) + 80y (x) - 242y (x) + 419y (x) - 416y (x) +--R +--R + +--R , +--R 220y (x) - 48y(x) +--R +--R = +--R 0 +--R Type: Equation Expression Integer +--E 119 + +--S 120 of 177 solve(ode,y,x) +--R +--R +--R 4x 3x 2x 2x x x 2 x +--R (3) [particular= 0,basis= [%e ,%e ,%e ,x %e ,%e ,x %e ,x %e ]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 120 --- 38 )clear all + +--S 121 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 121 + +--S 122 of 177 ode := D(y x,x,4) -4/x^2*D(y x,x,2) + 8/x^3*D(y x,x) -8/x^4*D(y x,x) = 0 +--R +--R +--R 4 (iv) 2 ,, , +--R x y (x) - 4x y (x) + (8x - 8)y (x) +--R +--R (2) --------------------------------------= 0 +--R 4 +--R x +--R Type: Equation Expression Integer +--E 122 + +--S 123 of 177 solve(ode,y,x) +--R +--R +--R (3) [particular= 0,basis= [1]] +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 123 --- 39 )clear all + +--S 124 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 124 + +--S 125 of 177 ode := (1+x+x^2)*D(y x,x,3) + (3+6*x)*D(y x,x,2) +6*D(y x,x) = 6*x +--R +--R +--R 2 ,,, ,, , +--R (2) (x + x + 1)y (x) + (6x + 3)y (x) + 6y (x)= 6x +--R +--R Type: Equation Expression Integer +--E 125 + +--S 126 of 177 solve(ode,y,x) +--R +--R +--R 4 +--R x - 4 1 x + 1 +--R (3) [particular= ------------,basis= [----------,----------,1]] +--R 2 2 2 +--R 4x + 4x + 4 x + x + 1 x + x + 1 +--RType: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +--E 126 --- 40 )clear all + +--S 127 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 127 + +--S 128 of 177 ode := (D(y x,x)^2 +1)*D(y x,x,3) - 3*D(y x,x)*D(y x,x,2) = 0 +--R +--R +--R , 2 ,,, , ,, +--R (2) (y (x) + 1)y (x) - 3y (x)y (x)= 0 +--R +--R Type: Equation Expression Integer +--E 128 + +--S 129 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R parseLODE: not a linear ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 129 --- 41 )clear all + +--S 130 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 130 + +--S 131 of 177 ode := 3*D(y x,x,2)*D(y x,x,4) - 5*D(y x,x,3)^2 = 0 +--R +--R +--R ,, (iv) ,,, 2 +--R (2) 3y (x)y (x) - 5y (x) = 0 +--R +--R Type: Equation Expression Integer +--E 131 + +--S 132 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R parseLODE: not a linear ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 132 -- Special Equations --- 42 )clear all + +--S 133 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 133 + +--S 134 of 177 ode := D(y t,t) + a*y(t-1) = 0 +--R +--R +--R , +--R (2) y (t) + a y(t - 1)= 0 +--R +--R Type: Equation Expression Integer +--E 134 + +--S 135 of 177 solve(ode,y,t) +--R +--R +--R t +--R ++ +--I (3) | a y(%J - 1)d%J + y(t) +--R ++ +--R Type: Union(Expression Integer,...) +--E 135 --- 43 )clear all + + +--S 136 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 136 + +--S 137 of 177 ode := D(y(x,a),x) = a*y(x,a) +--R +--R +--R (2) y (x,a)= a y(x,a) +--R ,1 +--R Type: Equation Expression Integer +--E 137 + +--S 138 of 177 solve(ode,y,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R parseODE: equation has order 0 +--R +--R Continuing to read the file... +--R +--E 138 --- 44 )clear all + + +--S 139 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 139 + +--S 140 of 177 ode := D(y x,x,4) = sin(x) +--R +--R +--R (iv) +--R (2) y (x)= sin(x) +--R +--R Type: Equation Expression Integer +--E 140 + +--S 141 of 177 solve(ode,y,x=0,[0,0,0,0]) +--R +--R +--R 3 +--R 6sin(x) + x - 6x +--R (3) ----------------- +--R 6 +--R Type: Union(Expression Integer,...) +--E 141 --- 45 )clear all + +--S 142 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 142 + +--S 143 of 177 ode := x*D(y x,x,2) + D(y x,x) +2*x*y(x) =0 +--R +--R +--R ,, , +--R (2) xy (x) + y (x) + 2x y(x)= 0 +--R +--R Type: Equation Expression Integer +--E 143 + +--S 144 of 177 solve(ode,y,x=0,[1,0]) +--R +--R +--R (3) "failed" +--R Type: Union("failed",...) +--E 144 --- 46 )clear all + +--S 145 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 145 + +--S 146 of 177 ode := x*D(y x,x)^2 -(y x)^2 + 1 = 0 +--R +--R +--R , 2 2 +--R (2) x y (x) - y(x) + 1= 0 +--R +--R Type: Equation Expression Integer +--E 146 + +--S 147 of 177 solve(ode,y,x=0,[1]) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R getlincoeff: not an appropriate ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 147 --- 47 )clear all + +--S 148 of 177 y := operator 'y +--R +--R +--R (1) y +--R Type: BasicOperator +--E 148 + +--S 149 of 177 ode := D(y x,x,2) + y(x)*D(y x,x)^3 = 0 +--R +--R +--R ,, , 3 +--R (2) y (x) + y(x)y (x) = 0 +--R +--R Type: Equation Expression Integer +--E 149 + +--S 150 of 177 solve(ode,y,x=0,[0,2]) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R getlincoeff: not an appropriate ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 150 -- Systems Of equations --- 48 )clear all + +--S 151 of 177 x := operator 'x +--R +--R +--R (1) x +--R Type: BasicOperator +--E 151 + +--S 152 of 177 y := operator 'y +--R +--R +--R (2) y +--R Type: BasicOperator +--E 152 + +--S 153 of 177 z := operator 'z +--R +--R +--R (3) z +--R Type: BasicOperator +--E 153 + +--S 154 of 177 odes := [D(x t,t) = -3*y(t)*z(t), D(y t,t) = 3*x(t)*z(t), D(z t,t) = -x(t)*y(t)] +--R +--R +--R , , , +--R (4) [x (t)= - 3y(t)z(t),y (t)= 3x(t)z(t),z (t)= - x(t)y(t)] +--R +--R Type: List Equation Expression Integer +--E 154 + +--S 155 of 177 solve(odes,[x,y,z],t) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R getfreelincoeff: not a linear ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 155 --- 49 )clear all + +--S 156 of 177 x := operator 'x +--R +--R +--R (1) x +--R Type: BasicOperator +--E 156 + +--S 157 of 177 y := operator 'y +--R +--R +--R (2) y +--R Type: BasicOperator +--E 157 + +--S 158 of 177 a := operator 'a +--R +--R +--R (3) a +--R Type: BasicOperator +--E 158 + +--S 159 of 177 b := operator 'b +--R +--R +--R (4) b +--R Type: BasicOperator +--E 159 + +--S 160 of 177 odes := [D(x t,t) = a(t)*((y t)^2 - (x t)^2) + 2*b(t)*x(t)*y(t) + 2*c*x(t), D(y t,t) = b(t)*((y t)^2 - (x t)^2) - 2*a(t)*x(t)*y(t) + 2*c*y(t)] +--R +--R +--R (5) +--R , 2 2 +--R [x (t)= a(t)y(t) + 2b(t)x(t)y(t) - a(t)x(t) + 2c x(t), +--R +--R , 2 2 +--R y (t)= b(t)y(t) + (- 2a(t)x(t) + 2c)y(t) - b(t)x(t) ] +--R +--R Type: List Equation Expression Integer +--E 160 + +--S 161 of 177 solve(odes,[x,y],t) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R getlincoeff: not an appropriate ordinary differential equation +--R +--R Continuing to read the file... +--R +--E 161 --- 50 )clear all + +--S 162 of 177 x := operator 'x +--R +--R +--R (1) x +--R Type: BasicOperator +--E 162 + +--S 163 of 177 y := operator 'y +--R +--R +--R (2) y +--R Type: BasicOperator +--E 163 + +--S 164 of 177 odes := [D(x t,t) = x(t)*(1+cos(t)/(2+sin(t))), D(y t,t) = x(t) - y(t)] +--R +--R +--R , x(t)sin(t) + x(t)cos(t) + 2x(t) , +--R (3) [x (t)= -------------------------------,y (t)= - y(t) + x(t)] +--R sin(t) + 2 +--R Type: List Equation Expression Integer +--E 164 + +--S 165 of 177 solve(odes,[x,y],t) +--R +--R +--R (4) "failed" +--R Type: Union("failed",...) +--E 165 --- 51 )clear all + +--S 166 of 177 x := operator 'x +--R +--R +--R (1) x +--R Type: BasicOperator +--E 166 + +--S 167 of 177 y := operator 'y +--R +--R +--R (2) y +--R Type: BasicOperator +--E 167 + +--S 168 of 177 odes := [D(x t,t) = 9*x(t) + 2*y(t), D(y t,t) = x(t) + 8*y(t)] +--R +--R +--R , , +--R (3) [x (t)= 2y(t) + 9x(t),y (t)= 8y(t) + x(t)] +--R +--R Type: List Equation Expression Integer +--E 168 + +--S 169 of 177 solve(odes,[x,y],t) +--R +--R +--R 10t +--R 10t %e 7t 7t +--R (4) [particular= [0,0],basis= [[%e ,-----],[%e ,- %e ]]] +--R 2 +--RType: Union(Record(particular: Vector Expression Integer,basis: List Vector Expression Integer),...) +--E 169 --- 52 )clear all + +--S 170 of 177 x := operator 'x +--R +--R +--R (1) x +--R Type: BasicOperator +--E 170 + +--S 171 of 177 y := operator 'y +--R +--R +--R (2) y +--R Type: BasicOperator +--E 171 + +--S 172 of 177 odes := [D(x t,t) - x(t) - 2*y(t) = 0, D(x t,t,2) - 2*D(y t,t) = 2*t - cos(2*t)] +--R +--R +--R , ,, , +--R (3) [x (t) - 2y(t) - x(t)= 0,x (t) - 2y (t)= - cos(2t) + 2t] +--R +--R Type: List Equation Expression Integer +--E 172 + +--S 173 of 177 solve(odes,[x,y],t) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R solve: not a first order linear system +--R +--R Continuing to read the file... +--R +--E 173 --- 53 )clear all + +--S 174 of 177 y1 := operator 'y1 +--R +--R +--R (1) y1 +--R Type: BasicOperator +--E 174 + +--S 175 of 177 y2 := operator 'y2 -odes := [D(y1 x,x) = -1/(x*(x^2 + 1))*y1(x) + 1/(x^2*(x^2 + 1))*y2(x)+1/x, +--R +--R +--R (2) y2 +--R Type: BasicOperator +--E 175 + +--S 176 of 177 +odes := [D(y1 x,x) = -1/(x*(x^2 + 1))*y1(x) + 1/(x^2*(x^2 + 1))*y2(x)+1/x,_ D(y2 x,x) = -x^2/(x^2 + 1)*y1(x) + (2*x^2+1)/x/(x^2+1)*y2(x)+1] +--R +--R +--R (3) +--R 3 2 3 3 +--R , y2(x) - x y1(x) + x + x , (2x + 1)y2(x) - x y1(x) + x + x +--R [y1 (x)= ------------------------,y2 (x)= ---------------------------------] +--R 4 2 3 +--R x + x x + x +--R Type: List Equation Expression Integer +--E 176 + +--S 177 of 177 solve(odes,[y1,y2],x) +--R +--R +--R 1 2 +--R (4) [particular= [log(x) - 1,x log(x) - x],basis= [[-,- x ],[1,x]]] +--R x +--RType: Union(Record(particular: Vector Expression Integer,basis: List Vector Expression Integer),...) +--E 177 + +)spool +)lisp (bye) \end{chunk} \eject