View of /trunk/NationalProblemLibrary/UMN/calculusStewartCCC/s_17_2_prob01.pg

    1 #DESCRIPTION
    2 ##  Calculus: Second-order nonhomogeneous linear equations
    3 ##ENDDESCRIPTION
    4 
    5 ##KEYWORDS('calculus', 'differential equations', 'linear equations', 'second-order', 'nonhomogeneous', 'method of undetermined coefficients')
    6 
    7 ## DBsubject('Calculus')
    8 ## DBchapter('Second-Order Differential Equations')
    9 ## DBsection('Nonhomogeneous Linear Equations')
   10 ## Date('06/21/2011')
   11 ## Author('Justin Sukiennik')
   12 ## Institution('University of Minnesota')
   13 ## TitleText1('Calculus: Concepts and Contexts')
   14 ## EditionText1('4 Custom UMTYMP Ed.')
   15 ## AuthorText1('Stewart')
   16 ## Section1('17.2')
   17 ## Problem1('')
   18 
   19 #####################################################################
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23   "PGstandard.pl",
   24   "MathObjects.pl",
   25   "PGcourse.pl",
   26 );
   27 
   28 #####################################################################
   29 install_problem_grader(~~&std_problem_grader);
   30 
   31 $showPartialCorrectAnswers = 0;
   32 
   33 TEXT(beginproblem());
   34 
   35 #####################################################################
   36 
   37 Context("Numeric");
   38 Context()->strings->add(A=>{},B=>{},C=>{},D=>{},E=>{},F=>{});
   39 
   40 #####################################################################
   41 
   42 $a = Compute("2");
   43 $b = random(1,2,1);
   44 
   45 #####################################################################
   46 
   47 if ($b ==1){
   48 $f = "\frac{d^2y}{dx^2}+4y=x-\frac{x^2}{20}";
   49 $ans1 = "A";
   50 
   51 $g = "\frac{d^2y}{dx^2}+6 \frac{dy}{dx}+8y=e^{2x}";
   52 $ans2 = "B";
   53 }
   54 if ($b ==2){
   55 $f = "\frac{d^2y}{dx^2}-5 \frac{dy}{dx}+6y=e^{2x}";
   56 $ans1 = "E";
   57 
   58 $g = "\frac{d^2y}{dx^2}+4y=-3x^2+2x+3";
   59 $ans2 = "A";
   60 }
   61 
   62 #####################################################################
   63 
   64 $c = random(1,2,1);
   65 
   66 if ($c ==1){
   67 $h = "y''+4y'+20y = -3 \sin 2x";
   68 $ans3 = "C";
   69 }
   70 if ($c ==2){
   71 $h = "y''+4y'+13y = 3 \cos 2x";
   72 $ans3 = "C";
   73 }
   74 
   75 #####################################################################
   76 
   77 $d = random(1,2,1);
   78 
   79 if ($d ==1){
   80 $i = "y''-2y'-15y = e^{3x}\cos 2x";
   81 $ans4 = "F";
   82 }
   83 if ($d ==2){
   84 $i = "y''-2y'-15y = 3x\cos 2x";
   85 $ans4 = "D";
   86 }
   87 
   88 #####################################################################
   89 
   90 Context()->texStrings;
   91 BEGIN_TEXT
   92 Match the following guess solutions \(y_p\) for the $BITALIC method of undetermined coefficients$EITALIC with the second-order nonhomogeneous linear equations below. $PAR
   93 $BCENTER
   94 $BBOLD A. $EBOLD \(\displaystyle y_p(x) = Ax^2+Bx+C \), $SPACE
   95 $BBOLD B. $EBOLD \(\displaystyle y_p(x) = Ae^{$a x} \), $SPACE
   96 $BBOLD C. $EBOLD \(\displaystyle  y_p(x) = A \cos $a x + B \sin $a x\),$BR
   97 $BBOLD D. $EBOLD \(\displaystyle  y_p(x) = (Ax + B)\cos $a x + (Cx+D)\sin $a x \) $SPACE
   98 $BBOLD E. $EBOLD \(\displaystyle  y_p(x) = A x e^{$a x},\)
   99 $SPACE and $SPACE
  100 $BBOLD F. $EBOLD \(\displaystyle  y_p(x) = e^{3x}(A \cos $a x + B \sin $a x)\)
  101 $ECENTER
  102 $PAR
  103 $HR
  104 $BBOLD 1. $EBOLD\{ans_rule(3)\} \(\displaystyle $f \)
  105 $PAR
  106 $BBOLD 2. $EBOLD\{ans_rule(3)\} \(\displaystyle $g\)
  107 $PAR
  108 $BBOLD 3. $EBOLD\{ans_rule(3)\} \(\displaystyle $h\)
  109 $PAR
  110 $BBOLD 4. $EBOLD\{ans_rule(3)\} \(\displaystyle $i\)
  111 $PAR
  112 $HR
  113 END_TEXT
  114 Context()->normalStrings;
  115 
  116 #####################################################################
  117 
  118 ANS(str_cmp($ans1,"ignore_case"));
  119 ANS(str_cmp($ans2,"ignore_case"));
  120 ANS(str_cmp($ans3,"ignore_case"));
  121 ANS(str_cmp($ans4,"ignore_case"));
  122 
  123 ENDDOCUMENT();        # This should be the last executable line in the problem.