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# View of /trunk/NationalProblemLibrary/Rochester/setDiffEQ9Linear2ndOrderHomog/ur_de_9_18.pg

Fri Apr 28 13:46:21 2006 UTC (7 years ago) by jjholt
File size: 1312 byte(s)
```Added tags.  --JH
```

```    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('differential equation' 'second order' 'linear')
6 ## Tagged by tda2d
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Second-Order Differential Equations')
10 ## DBsection('Second-Order Linear Equations')
11 ## Date('')
12 ## Author('')
13 ## Institution('Rochester')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20
21 DOCUMENT() ;
22
24 "PG.pl",
25 "PGbasicmacros.pl",
26 "PGchoicemacros.pl",
28 "PGauxiliaryFunctions.pl",
29 "PGdiffeqmacros.pl",
30 ) ;
31 ############
32
33
34 TEXT(beginproblem()) ;
35
37
38 \$r1 = random(2,9,1);
39 \$r2 = random(-9,-1,1);
40 while((\$r1 + \$r2 == 0) or (\$r1 + \$r2 == 1) or (\$r1 + \$r2 == 2)) { \$r2 = random(-9,-1,1); }
41
42 \$a = 1 - \$r1 - \$r2;
43 \$b = \$r1 * \$r2;
44
45 \$d = random(-10,10,1);
46 \$c = random(-10,10,1);
47 while ((\$c == \$r1 * \$d) or (\$c == \$r2 * \$d)) { \$c = random(-10,10,1); }
48
49 \$eq = FEQ("x^2 y'' + \$a x y' + \$b y = 0");
50
51 \$k1 = (\$c - \$r2 * \$d)/(\$r1 - \$r2);
52 \$k2 = (\$c - \$r1 * \$d)/(\$r2 - \$r1);
53
54 \$ans = FEQ("\$k1 * x**\$r1 + \$k2 * x**\$r2");
55
56 BEGIN_TEXT
57
58 Find \(y\) as a function of \(x\) if \[ \$eq, \]
59 \$BR
60 \( y(1)=\$d, \ \ y'(1)=\$c. \)
61 \$BR
62 \(y=\)\{ans_rule(20)\}
63
64 END_TEXT
65
66 ANS(fun_cmp(\$ans));
67
68 ENDDOCUMENT() ;
69
70
71
72
73
74
75 ##################################################
```