[npl] / trunk / NationalProblemLibrary / Rochester / setDiffEQ10Linear2ndOrderNonhom / ur_de_10_9.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /trunk/NationalProblemLibrary/Rochester/setDiffEQ10Linear2ndOrderNonhom/ur_de_10_9.pg

Fri Apr 28 13:46:21 2006 UTC (7 years ago) by jjholt
File size: 2225 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 # root of the characteristic equation
33 $b = random(2,6,1); 34$d = $b**2; 35$c = non_zero_random(-5,5,1) * 2 * $b; 36 # initial guess is Atcos(bt) + Btsin(bt) 37$A = -($c/(2*$b));
38
39 $ans = "$A * t * cos($b*t) "; 40 41 TEXT(beginproblem()) ; 42 43$showPartialCorrectAnswers = 1 ;
44 #Problem written by Dr. Lesh
45
46 BEGIN_TEXT
47
48 Find a particular solution to
49 $y'' + d y = c \sin(b t) .$
50 $BR 51 $$y_{p} =$$ \{ans_rule(60)\} 52 53 END_TEXT 54$homogeneous = "a*sin($b*t) + b*cos($b*t)";
55 ANS(fun_cmp("$ans +$homogeneous", var => 't',  params => ['a', 'b']) );
56
57 ENDDOCUMENT() ;
58
59
60
61
62
63
64
65
66
67
68
69 ##################################################
70 my $XML_INFORMATION = <<'END_OF_XML_TRAILER_INFO'; 71 <?xml version="1.0"?> 72 <metaPGdata> 73 <author>Kathryn Lesh</author> 74 <course>Math 3860 Toledo</course> 75 <description>Differential equations 76 ay'' + by' + cy = 0, 77$a,$b,$c should be integers.
78 undetermined coeff</description>
79   <fullPath>kl/prob16.pg</fullPath>
80   <institution>University of Toledo</institution>
81   <keywords>Differential Equation, undetermined coefficients,
82 second order linear, constant coefficients,</keywords>
83   <libraryPath>setDESOLinear/6.pg</libraryPath>
85   <modified><dateTime.iso8601>20000718T14:15:38</dateTime.iso8601></modified>
86   <msgNum>422</msgNum>
87   <pgProblem>true</pgProblem>
88   <preface></preface>
89   <problemVariants></problemVariants>
90   <probNum></probNum>
91   <psvn></psvn>
92   <revisedVersions></revisedVersions>
93   <setName>DESOLinear</setName>
94   <titleRoot>6</titleRoot>
95   </metaPGdata>
96
97 END_OF_XML_TRAILER_INFO
98 ##################################################