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# View of /branches/CSUN/DifferentalEquations/CSUN-Series_Solution1.pg

Sat Jul 17 18:26:38 2010 UTC (2 years, 10 months ago) by david protas
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`trying to copy file to the directory Calculus in the server`

```    1 ##DESCRIPTION
2 #  Power series solution of a differential equation
3 ##ENDDESCRIPTION
4
5 ## DBsubject('Calculus')
6 ## DBchapter('Second-Order Differential Equations')
7 ## DBsection('Second-Order Linear Equations')
8 ## KEYWORDS('power series solution')
9 ## Author('David Protas')
10 ## Institution('CSUN')
11
12 DOCUMENT();
13
15 "PGbasicmacros.pl",
17 "PGauxiliaryFunctions.pl"
18 );
19
20 TEXT(&beginproblem);
22
23 \$a = random(1, 10);
24
25 \$abs = "\$g*sqrt((\$a)**2 + (\$b)**2 + (\$c)**2)";
26
27 BEGIN_TEXT
28
29 Find two linearly independent solutions of \( y'' + \$a xy = 0 \) of the form
30 \$BR\$BR
31 \( y_1 = 1 + a_3 x^3 + a_6 x^6 + \cdots \)
32 \$BR\$BR
33 \( y_2 = x + b_4 x^4 + b_7 x^7 + \cdots \)
34 \$BR\$BR
35 Enter the first few coefficients:
36 \$BR\$BR
37 \( a_3 = \)  \{ans_rule(15)\} \$BR
38 \( a_6 = \)  \{ans_rule(15)\} \$BR\$BR
39 \( b_4 = \)  \{ans_rule(15)\} \$BR
40 \( b_7 = \)  \{ans_rule(15)\}
41
42 END_TEXT
43
44 ANS(num_cmp("-\$a/6"));
45 ANS(num_cmp("\$a^2/180"));
46 ANS(num_cmp("-\$a/12"));
47 ANS(num_cmp("\$a^2/504"));
48
49 ENDDOCUMENT();
```