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| 1 : | jj | 145 | ## DESCRIPTION |
| 2 : | jjholt | 184 | ## Calculus |
| 3 : | jj | 145 | ## ENDDESCRIPTION |
| 4 : | |||
| 5 : | jjholt | 184 | ## 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 : | jj | 145 | DOCUMENT() ; |
| 21 : | |||
| 22 : | loadMacros( | ||
| 23 : | "PG.pl", | ||
| 24 : | "PGbasicmacros.pl", | ||
| 25 : | "PGchoicemacros.pl", | ||
| 26 : | "PGanswermacros.pl", | ||
| 27 : | "PGauxiliaryFunctions.pl", | ||
| 28 : | "PGdiffeqmacros.pl", | ||
| 29 : | |||
| 30 : | ) ; | ||
| 31 : | $r = random(-9,-1,1) ; | ||
| 32 : | $u = random(1,9,1) ; | ||
| 33 : | $s = $r + $u ; | ||
| 34 : | $B = - $r - $s ; | ||
| 35 : | $C = $r *$s ; | ||
| 36 : | $k = random(1,3,1) ; | ||
| 37 : | $rr = $s + $k ; | ||
| 38 : | $q0 = random(1,9,1) ; | ||
| 39 : | $qq0 = $q0 ; | ||
| 40 : | $q0 = $q0 *($rr - $r)*$k ; | ||
| 41 : | $q1 =0 ; | ||
| 42 : | $q2 = 0 ; | ||
| 43 : | $A =1 ; | ||
| 44 : | $m = random(1,9,1) ; | ||
| 45 : | $n = random(1,9,1) ; | ||
| 46 : | ################ | ||
| 47 : | |||
| 48 : | $L = diffop($A,$B,$C) ; | ||
| 49 : | $Exp = "e^{$rr t}"; | ||
| 50 : | $rhs = "$q0 \,$Exp " ; | ||
| 51 : | |||
| 52 : | $y = undeterminedExp ($A,$B,$C,$rr,$q0,$q1,$q2) ; | ||
| 53 : | $z = ivy($A,$B,$C,$m - $qq0,$n - $rr *$qq0 ) ; | ||
| 54 : | $ans = " $y + $z " ; | ||
| 55 : | TEXT(beginproblem()) ; | ||
| 56 : | $showPartialCorrectAnswers = 1 ; | ||
| 57 : | |||
| 58 : | BEGIN_TEXT | ||
| 59 : | |||
| 60 : | Find the solution of | ||
| 61 : | \[ $L = $rhs \] | ||
| 62 : | with \( y(0) = $m \) and \( y'(0) = $n .\) | ||
| 63 : | $BR | ||
| 64 : | \(y = \) \{ans_box(4,80)\} | ||
| 65 : | |||
| 66 : | END_TEXT | ||
| 67 : | |||
| 68 : | ANS(fun_cmp($ans, vars=>"t")) ; | ||
| 69 : | |||
| 70 : | ENDDOCUMENT() ; | ||
| 71 : | ####### | ||
| 72 : | |||
| 73 : | |||
| 74 : | |||
| 75 : | ################################################## | ||
| 76 : | my $XML_INFORMATION = <<'END_OF_XML_TRAILER_INFO'; | ||
| 77 : | <?xml version="1.0"?> | ||
| 78 : | <metaPGdata> | ||
| 79 : | <author>Webwork Team</author> | ||
| 80 : | <course>MTH163</course> | ||
| 81 : | <description>Differential equations solves $A y'' + $B y' + $C y = $q0 exp($r t), | ||
| 82 : | |||
| 83 : | $A, $B, $C, $q0, $q1, $q2, $r are integers; | ||
| 84 : | $A not zero; | ||
| 85 : | $r is not a root of the char. poly..</description> | ||
| 86 : | <fullPath>setUndeterminedCoefficients/1.pg</fullPath> | ||
| 87 : | <institution>University of Rochester</institution> | ||
| 88 : | <keywords>Differential Equation, | ||
| 89 : | Inhomogeneous, | ||
| 90 : | Undetermined coefficients, | ||
| 91 : | second order linear, | ||
| 92 : | constant coefficients</keywords> | ||
| 93 : | <libraryPath>setUndeterminedCoefficients/1.pg</libraryPath> | ||
| 94 : | <libraryURL>http://webhost.math.rochester.edu/mth163lib/discuss/msgReader$442</libraryURL> | ||
| 95 : | <modified><dateTime.iso8601>20000719T09:39:52</dateTime.iso8601></modified> | ||
| 96 : | <msgNum>442</msgNum> | ||
| 97 : | <pgProblem>true</pgProblem> | ||
| 98 : | <preface></preface> | ||
| 99 : | <problemVariants></problemVariants> | ||
| 100 : | <probNum></probNum> | ||
| 101 : | <psvn></psvn> | ||
| 102 : | <revisedVersions></revisedVersions> | ||
| 103 : | <setName>UndeterminedCoefficients</setName> | ||
| 104 : | <titleRoot>1</titleRoot> | ||
| 105 : | </metaPGdata> | ||
| 106 : | |||
| 107 : | END_OF_XML_TRAILER_INFO | ||
| 108 : | ################################################## | ||
| 109 : |
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