[npl] / trunk / NationalProblemLibrary / Rochester / setDiffEQ9Linear2ndOrderHomog / ur_de_9_9.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /trunk/NationalProblemLibrary/Rochester/setDiffEQ9Linear2ndOrderHomog/ur_de_9_9.pg

Fri Apr 28 13:46:21 2006 UTC (7 years ago) by jjholt
File size: 2416 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 DOCUMENT() ;
21
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "PGauxiliaryFunctions.pl",
28 "PGdiffeqmacros.pl",
29 ) ;
30 ###
31 $aa = random(2,11,1) ; 32$a = $aa **2 ; 33$B = random(-10,10,1) ;
34 $e = random(1,9,1) ; 35$eps = random(-1,1,1) ;
36 $b = 2*$B*$aa ; 37$c = $B *$B - $eps * ($e **2) ;
38 $m = random(1,9,1) ; 39$n = random(1,9,1) ;
40
41 ####################
42
43
44 $L = diffop($a,$b,$c,$m,$n) ;
45 $ans = ivy($a,$b,$c,$m,$n) ;
46
47 TEXT(beginproblem()) ;
48
49 $showPartialCorrectAnswers = 1 ; 50 51 BEGIN_TEXT 52 53 Find $$y$$ as a function of $$t$$ if$BR
54 $L = 0,$
55 $$y(0) = m, \quad y'(0) = n .$$ $BR 56 $$y =$$ \{ans_rule(170)\} 57$BR
58 Note: This problem cannot interpret complex numbers.  You may need to simplify your answer before submitting it.
59
60 END_TEXT
61
62 ANS(fun_cmp($ans, vars=>"t")) ; 63 64 ENDDOCUMENT() ; 65 66 67 68 69 70 71 ################################################## 72 my$XML_INFORMATION = <<'END_OF_XML_TRAILER_INFO';
73 <?xml version="1.0"?>
74 <metaPGdata>
75   <author>David Prill</author>
76   <course>MTH163</course>
77   <description>Differential equations
78 ay'' + by' + cy =  0,
79 $a,$b, $c should be integers and$a>0.
80 Gaussian rational roots problem of random type may be asked repeatedly to get random types</description>
81   <fullPath>setDESOLinear/8.pg</fullPath>
82   <institution>University of Rochester</institution>
83   <keywords>Differential Equation, Initial value problem,
84 second order linear, constant coefficients,
85 quadratic formula, Gaussian rational roots</keywords>
86   <libraryPath>setDESOLinear/8.pg</libraryPath>
88   <modified><dateTime.iso8601>20000718T14:21:56</dateTime.iso8601></modified>
89   <msgNum>425</msgNum>
90   <pgProblem>true</pgProblem>
91   <preface></preface>
92   <problemVariants></problemVariants>
93   <probNum></probNum>
94   <psvn></psvn>
95   <revisedVersions></revisedVersions>
96   <setName>DESOLinear</setName>
97   <titleRoot>8</titleRoot>
98   </metaPGdata>
99
100 END_OF_XML_TRAILER_INFO
101 ##################################################
102


 aubreyja at gmail dot com ViewVC Help Powered by ViewVC 1.0.9