1/* Filename <name>.mac
2
3   ***************************************************************
4   *							         *
5   *                     <package name>                          *
6   *                <functionality description>                  *
7   *                                                             *
8   *          from: Computer Algebra in Applied Math.            *
9   *                   by Rand (Pitman,1984)                     *
10   *                Programmed by Richard Rand                   *
11   *      These files are released to the public domain          *
12   *            						 *
13   ***************************************************************
14*/ /*
15
16(d5) This program generates the Taylor series solution
17
18
19to the 1st order ODE:
20
21
22                    Y' = F(X,Y)
23
24
25for an arbitrary initial condition at X = 0.
26
27
28To call it, type:
29
30
31                      SOLUTION()
32
33*/
34
35
36solution():=(input(),u:z,v:f,
37	 for i thru m do (u:u+evaluate(v)*x^i/i!,v:deriv(v)),output())$
38input():=(m:read("ENTER DEGREE OF TRUNCATION"),
39      f:read("ENTER RIGHT HAND SIDE OF ODE Y'=F(X,Y)"),print(" "),
40      print("Y' =",f),print(" "),z:read("ENTER INITIAL VALUE OF Y"))$
41deriv(g):=diff(g,x)+diff(g,y)*f$
42evaluate(g):=ev(g,x:0,y:z)$
43output():=print("Y =",u)$
44