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Mon Feb 20 04:30:39 2012 UTC (15 months ago) by david protas
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```    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();
14 "PGstandard.pl",
15   "Parser.pl",
16   "PGcourse.pl",
18   "PGbasicmacros.pl",
19 );
20
21 Context("Numeric");
22 TEXT(&beginproblem);
24
25 \$a = random(1, 10);
26 \$abs = "\$g*sqrt((\$a)**2 + (\$b)**2 + (\$c)**2)";
27
28 Context()->texStrings;
29 BEGIN_TEXT
30
31 Find two linearly independent solutions of \( y'' + \$a xy = 0 \) of the form
32 \$BR\$BR
33 \( y_1 = 1 + a_3 x^3 + a_6 x^6 + \cdots \)
34 \$BR\$BR
35 \( y_2 = x + b_4 x^4 + b_7 x^7 + \cdots \)
36 \$BR\$BR
37 Enter the first few coefficients:
38 \$BR\$BR
39 \( a_3 = \)  \{ans_rule(15)\} \$BR
40 \( a_6 = \)  \{ans_rule(15)\} \$BR\$BR
41 \( b_4 = \)  \{ans_rule(15)\} \$BR
42 \( b_7 = \)  \{ans_rule(15)\}
43
44 END_TEXT
45
46 Context()->normalStrings;
47 ANS(num_cmp("-\$a/6"));
48 ANS(num_cmp("\$a^2/180"));
49 ANS(num_cmp("-\$a/12"));
50 ANS(num_cmp("\$a^2/504"));
51
52 ENDDOCUMENT();
```