[npl] / trunk / NationalProblemLibrary / Rochester / setDiffEQ9Linear2ndOrderHomog / ur_de_9_19.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /trunk/NationalProblemLibrary/Rochester/setDiffEQ9Linear2ndOrderHomog/ur_de_9_19.pg

Fri Apr 28 13:46:21 2006 UTC (7 years ago) by jjholt
File size: 1148 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 \$r = random(2,9,1);
34 \$sign = random(-1,1,2);
35 \$r = \$r * \$sign;
36
37 \$a = 1 - 2 * \$r;
38 \$b = \$r**2;
39
40 \$k1 = random(-10,10,1);
41 \$d = random(-5,5,1);
42 if ( \$d - \$r * \$k1 == 0 ) { \$d = \$d+1; }
43
44 \$k2 = \$d - \$r * \$k1;
45
46 \$eq = FEQ("x^2 y'' + \$a x y' + \$b y = 0");
47 \$ans = FEQ("x**\$r * (\$k1 + \$k2 * ln x)");
48
49 TEXT(beginproblem()) ;
50
52
53 BEGIN_TEXT
54
55 Find \(y\) as a function of \(x\) if \[ \$eq, \]
56 \$BR
57 \( y(1) = \$k1, \ \ y'(1) = \$d. \)
58 \$BR
59 \(y=\)\{ans_rule(20)\}
60
61 END_TEXT
62
63 ANS(fun_cmp(\$ans));
64
65 ENDDOCUMENT() ;
66
67
68
69
70
71
72 ##################################################
```