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

    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 
   22 loadMacros(
   23   "PG.pl",
   24   "PGbasicmacros.pl",
   25   "PGchoicemacros.pl",
   26   "PGanswermacros.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>
   84   <libraryURL>http://webhost.math.rochester.edu/mth163lib/discuss/msgReader$422</libraryURL>
   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 ##################################################