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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input zimmer.input}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+These examples come from Postel & Zimmermann's paper in the 5th Rhine
+Conference on Computer Algebra.
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{License}
+<<license>>=
+--Copyright The Numerical Algorithms Group Limited 1996.
+@
+<<*>>=
+<<license>>
+)set break resume
+
+-- First Order Equations
+
+-- 1
+
+u := operator 'u
+ode := (x^4-x^3)*D(u x,x) + 2*x^4*u(x) = x^3/3 + C
+solve(ode,u,x)
+
+-- 2
+)clear all
+
+u := operator 'u
+ode := -D(u x,x)/2 + u(x) = sin(x)
+solve(ode,u,x)
+
+-- 3
+)clear all
+
+y := operator 'y
+ode := D(y x,x) = y(x)/(y(x)*log(y(x)) + x)
+solve(ode,y,x)
+
+-- 4
+)clear all
+
+y := operator 'y
+ode := 2*y(x)*D(y x,x)^2 -2*x*D(y x,x)-y(x) = 0
+solve(ode,y,x)
+
+-- 5
+)clear all
+
+y := operator 'y
+ode := D(y x,x) + y(x) = y(x)^3*sin(x)
+solve(ode,y,x)
+
+-- 6
+)clear all 
+
+y := operator 'y
+P := operator 'P
+Q := operator 'Q
+ode := D(y x,x) + P(x)*y(x) = Q(x)*y(x)^n
+solve(ode,y,x)
+solve(eval(ode,n=1),y,x)
+solve(eval(ode,n=2),y,x)
+solve(eval(ode,n=%pi),y,x)
+solve(eval(ode,n=%e),y,x)
+solve(eval(ode,n=sqrt(2)),y,x)
+
+-- 7
+)clear all
+
+y := operator 'y
+ode := (x^2-1)*D(y x,x)^2 - 2*x*y(x)*D(y x,x)+(y x)^2 - 1 = 0
+solve(ode,y,x)
+
+-- 8
+)clear all
+
+y := operator 'y
+f := operator 'f
+g := operator 'g
+ode := f(x*D(y x,x) - y(x)) = g(D(y x,x))
+solve(ode,y,x)
+
+-- 9
+)clear all
+
+y := operator 'y
+ode := D(y x,x)  = (3*x^2-y(x)^2-7)/(exp(y(x))+2*x*y(x)+1)
+solve(ode,y,x)
+
+-- 10
+)clear all
+
+y := operator 'y
+ode := D(y x,x)  = (2*x^3*y(x) - (y x)^4)/(x^4 - 2*x*(y x)^3)
+solve(ode,y,x)
+
+-- 11
+)clear all
+
+y := operator 'y
+ode := D(y x,x)*(D(y x,x) + y(x)) = x*(x + y(x))
+solve(ode,y,x)
+
+-- 12
+)clear all
+
+y := operator 'y
+ode := D(y x,x) = x/(x^2*(y x)^2 + (y x)^5)
+solve(ode,y,x)
+
+-- 13
+)clear all
+
+y := operator 'y
+ode := y(x) = 2*x*D(y x,x) - a*D(y x,x)^3
+solve(ode,y,x)
+
+-- 14
+)clear all
+
+y := operator 'y
+ode := y(x) = 2*x*D(y x,x) - D(y x,x)^3
+solve(ode,y,x)
+
+-- 15
+)clear all
+
+y := operator 'y
+ode := D(y x,x) = exp(x)*(y x)^2 - y(x) + exp(-x)
+solve(ode,y,x)
+
+-- 16
+)clear all
+
+y := operator 'y
+ode := D(y x,x) = (y x)^2 - x*y(x) + 1
+solve(ode,y,x)
+
+-- 17
+)clear all
+
+y := operator 'y
+ode := D(y x,x) = (9*x^8 + 1)/((y x)^2 +1)
+solve(ode,y,x)
+
+-- 18
+)clear all
+
+y := operator 'y
+ode := y(x)=2*x*D(y x,x) + y(x)*D(y x,x)^2
+solve(ode,y,x)
+
+-- 19
+)clear all
+y := operator 'y
+ode := x = y(x)*D(y x,x) - x*D(y x,x)^2
+solve(ode,y,x)
+
+-- Second Order Equations
+
+-- 20
+)clear all
+y := operator 'y
+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
+solve(ode,y,x)
+
+-- 21
+)clear all
+u := operator 'u
+ode := (x^2 - x)*D(u x,x,2) + (2*x^2+4*x-3)*D(u x,x) + 8*x*u(x)=1
+solve(ode,u,x)
+
+-- 22
+)clear all
+w := operator 'w
+ode := (x^2 - x)*D(w x,x,2) + (1-2*x^2)*D(w x,x) + (4*x - 2)*w(x) = 0
+solve(ode,w,x)
+
+-- 23
+)clear all
+y := operator 'y
+ode := D(y x,x,2) - D(y x,x) = 2*y(x)*D(y x,x)
+solve(ode,y,x)
+
+-- 24
+)clear all
+y := operator 'y
+ode := D(y x,x,2)/y(x) - D(y x,x)^2/y(x)^2 -1 + y(x)^(-3) = 0
+solve(ode,y,x)
+
+-- 25
+)clear all
+y := operator 'y
+ode :=  D(y x,x,2) + 2*x*D(y x,x) = 2*x
+solve(ode,y,x)
+
+-- 26
+)clear all
+y := operator 'y
+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
+solve(ode,y,x)
+
+-- 27
+)clear all
+y := operator 'y
+ode := x*D(y x,x,2) = 2*y(x)*D(y x,x)
+solve(ode,y,x)
+
+-- 28
+)clear all
+y := operator 'y
+ode := (1-x)*(y(x)*D(y x,x,2) - D(y x,x)^2) + x^2*y(x)^2 = 0
+solve(ode,y,x)
+
+-- 29
+)clear all
+y := operator 'y
+ode := x*y(x)*D(y x,x,2) + x*D(y x,x)^2 + y(x)*D(y x,x) = 0
+solve(ode,y,x)
+
+-- 30
+)clear all
+y := operator 'y
+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
+solve(ode,y,x)
+
+-- 31 
+)clear all
+y := operator 'y
+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
+solve(ode,y,x)
+
+-- 32
+)clear all
+y := operator 'y
+ode := D(y x,x,2) - 2*x*D(y x,x) + 2*y(x) = 3
+solve(ode,y,x)
+
+-- 33
+)clear all
+y := operator 'y
+ode := sqrt(x)*D(y x,x,2) + 2*x*D(y x,x) + 3*y(x) = 0
+solve(ode,y,x)
+
+-- 34
+)clear all
+y := operator 'y
+ode := x^2*D(y x,x,2) + 3*x*D(y x,x) = 1/(x^4*y(x)^3)
+solve(ode,y,x)
+
+-- 35
+)clear all
+y := operator 'y
+ode := D(y x,x,2) - 2/x^2*y(x) = 7*x^4 +3*x^3
+solve(ode,y,x)
+
+-- 36
+)clear all
+y := operator 'y
+ode := D(y x,x,2) +y(x) = csc(x)
+solve(ode,y,x)
+
+-- Higher Order Equations
+
+-- 37
+)clear all
+y := operator 'y
+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
+solve(ode,y,x)
+
+-- 38
+)clear all
+y := operator 'y
+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
+solve(ode,y,x)
+
+-- 39
+)clear all
+y := operator 'y
+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
+solve(ode,y,x)
+
+-- 40
+)clear all
+y := operator 'y
+ode := (D(y x,x)^2 +1)*D(y x,x,3) - 3*D(y x,x)*D(y x,x,2) = 0
+solve(ode,y,x)
+
+-- 41
+)clear all
+y := operator 'y
+ode := 3*D(y x,x,2)*D(y x,x,4) - 5*D(y x,x,3)^2 = 0
+solve(ode,y,x)
+
+-- Special Equations
+
+-- 42
+)clear all
+y := operator 'y
+ode := D(y t,t) + a*y(t-1) = 0
+solve(ode,y,t)
+
+-- 43
+)clear all
+y := operator 'y
+ode := D(y(x,a),x) = a*y(x,a)
+solve(ode,y,x)
+
+-- 44
+)clear all
+y := operator 'y
+ode := D(y x,x,4) = sin(x)
+solve(ode,y,x=0,[0,0,0,0])
+
+-- 45
+)clear all
+y := operator 'y
+ode := x*D(y x,x,2) + D(y x,x) +2*x*y(x) =0
+solve(ode,y,x=0,[1,0])
+
+-- 46
+)clear all
+y := operator 'y
+ode := x*D(y x,x)^2 -(y x)^2 + 1 = 0
+solve(ode,y,x=0,[1])
+
+-- 47
+)clear all
+y := operator 'y
+ode := D(y x,x,2) + y(x)*D(y x,x)^3 = 0
+solve(ode,y,x=0,[0,2])
+
+-- Systems Of equations
+
+-- 48
+)clear all
+x := operator 'x
+y := operator 'y
+z := operator 'z
+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)]
+solve(odes,[x,y,z],t)
+
+-- 49
+)clear all
+x := operator 'x
+y := operator 'y
+a := operator 'a
+b := operator 'b
+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)]
+solve(odes,[x,y],t)
+
+-- 50
+)clear all
+x := operator 'x
+y := operator 'y
+odes := [D(x t,t) = x(t)*(1+cos(t)/(2+sin(t))), D(y t,t) = x(t) - y(t)]
+solve(odes,[x,y],t)
+
+-- 51
+)clear all
+x := operator 'x
+y := operator 'y
+odes := [D(x t,t) = 9*x(t) + 2*y(t), D(y t,t) = x(t) + 8*y(t)]
+solve(odes,[x,y],t)
+
+-- 52
+)clear all
+x := operator 'x
+y := operator 'y
+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)]
+solve(odes,[x,y],t)
+
+-- 53
+)clear all
+y1 := operator 'y1
+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,
+         D(y2 x,x) = -x^2/(x^2 + 1)*y1(x) + (2*x^2+1)/x/(x^2+1)*y2(x)+1]
+solve(odes,[y1,y2],x)
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}