## DESCRIPTION
## Calculus
## ENDDESCRIPTION

## KEYWORDS('differential equation' 'second order' 'linear' 'nonhomogeneous')
## Tagged by tda2d

## DBsubject('Calculus')
## DBchapter('Second-Order Differential Equations')
## DBsection('Nonhomogeneous Linear Equations')
## Date('')
## Author('')
## Institution('Rochester')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')

DOCUMENT() ;     

loadMacros(
	"PG.pl",
	"PGbasicmacros.pl",
	"PGchoicemacros.pl",
	"PGanswermacros.pl",
	"PGauxiliaryFunctions.pl",
	"PGdiffeqmacros.pl",

) ;
$r = random(-9,-1,1) ;
$u = random(1,9,1) ;
$s = $r + $u ;
$B = - $r - $s  ;
$C =  $r *$s  ;
$k = random(1,3,1) ;
$rr = $s + $k  ;
$q0 = random(1,9,1) ;
$qq0 = $q0 ;
$q0 = $q0 *($rr - $r)*$k  ;
$q1 =0 ;
$q2 = 0 ;
$A =1 ;
$m = random(1,9,1) ;
$n = random(1,9,1) ;
################

$L = diffop($A,$B,$C) ;
$Exp = "e^{$rr t}";
$rhs = "$q0 \,$Exp " ;

$y = undeterminedExp ($A,$B,$C,$rr,$q0,$q1,$q2) ;
$z = ivy($A,$B,$C,$m - $qq0,$n - $rr *$qq0 ) ;
$ans = " $y + $z " ;
TEXT(beginproblem()) ;
$showPartialCorrectAnswers = 1 ;

BEGIN_TEXT

Find the solution of  
\[ $L =  $rhs \]
with \( y(0) = $m \) and \( y'(0) = $n .\)
 $BR
\(y = \) \{ans_box(4,80)\}

END_TEXT

ANS(fun_cmp($ans, vars=>"t")) ;

ENDDOCUMENT() ;
#######

   

##################################################
my $XML_INFORMATION = <<'END_OF_XML_TRAILER_INFO';
<?xml version="1.0"?>
<metaPGdata>
        <author>Webwork Team</author>
        <course>MTH163</course>
        <description>Differential equations solves $A y'' + $B y' + $C y =   $q0 exp($r t),

$A, $B, $C, $q0, $q1, $q2, $r are integers;
$A not zero;
$r is not a root of the char. poly..</description>
        <fullPath>setUndeterminedCoefficients/1.pg</fullPath>
        <institution>University of Rochester</institution>
        <keywords>Differential Equation,
 Inhomogeneous,
Undetermined coefficients,
second order linear,
constant coefficients</keywords>
        <libraryPath>setUndeterminedCoefficients/1.pg</libraryPath>
        <libraryURL>http://webhost.math.rochester.edu/mth163lib/discuss/msgReader$442</libraryURL>
        <modified><dateTime.iso8601>20000719T09:39:52</dateTime.iso8601></modified>
        <msgNum>442</msgNum>
        <pgProblem>true</pgProblem>
        <preface></preface>
        <problemVariants></problemVariants>
        <probNum></probNum>
        <psvn></psvn>
        <revisedVersions></revisedVersions>
        <setName>UndeterminedCoefficients</setName>
        <titleRoot>1</titleRoot>
        </metaPGdata>

END_OF_XML_TRAILER_INFO
##################################################