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

    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 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.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>
   87   <libraryURL>http://webhost.math.rochester.edu/mth163lib/discuss/msgReader$425</libraryURL>
   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