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Fri Apr 28 13:46:21 2006 UTC (7 years ago) by jjholt
File size: 1366 byte(s)
```Added tags.  --JH
```

```    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('differential equation' 'second order' 'linear' 'nonhomogeneous')
6 ## Tagged by tda2d
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Second-Order Differential Equations')
10 ## DBsection('Nonhomogeneous Linear Equations')
11 ## Date('')
12 ## Author('')
13 ## Institution('Rochester')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20 DOCUMENT() ;
21
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "PGauxiliaryFunctions.pl",
28 "PGdiffeqmacros.pl",
29 ) ;
30 ############
31
32 \$r = random(2,9,1);
33 \$sign = random(-1,1,2);
34 \$r = \$r * \$sign;
35
36 \$a = 1 - 2 * \$r;
37 \$b = \$r**2;
38
39 \$c = random(-10,10,1);
40 \$d = random(-5,5,1);
41
42 \$m = random(2,9,1);
43 while (\$m * (\$m-1) + \$m * \$a + \$b == 0) { \$m = random(2,9,1);}
44
45 \$n = 1/(\$m * (\$m-1) + \$m * \$a + \$b);
46
47 \$c1 = \$c - \$n;
48
49 if ( \$d - \$r * \$c1 == 0 ) {
50   \$d = \$d+1;
51   \$c1 = \$c - \$n;
52 }
53
54 \$d1 = \$d - \$m * \$n;
55
56 \$k1 = \$c1;
57 \$k2 = \$d1 - \$r * \$c1;
58
59 \$eq = FEQ("x^2 y'' + \$a x y' + \$b y = x^\$m");
60 \$ans = FEQ("x**\$r * (\$k1 + \$k2 * ln x) + \$n x^\$m");
61
62 TEXT(beginproblem()) ;
63
65
66 BEGIN_TEXT
67
68 Find \(y\) as a function of \(x\) if
69 \[ \$eq, \]
70 \( y(1) = \$c, \ \ y'(1) = \$d. \)
71 \$BR
72 \(y=\) \{ans_rule(80)\}
73
74 END_TEXT
75
76 ANS(fun_cmp(\$ans));
77
78 ENDDOCUMENT() ;
79
80
81
82
83
84
85 ##################################################
```