webwork-open-problem-library/Contrib/METU-NCC/Diff_Eq/high-order-linear_1.pg at e9fe180d42872fcbfd51cab022b47f433d4e1aac · openwebwork/webwork-open-problem-library · GitHub

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## DESCRIPTION
## Differential Equations.
## ENDDESCRIPTION

## DBsubject(Differential equations)
## DBchapter(Higher order differential equations)
## DBsection(Linear, constant coefficients, homogeneous)
## Date(24/11/2015)
## Institution(METU-NCC)
## Author(Benjamin Walter)

##################################
#  Initialization

DOCUMENT();
loadMacros(
  "PGstandard.pl",
  "PGmatrixmacros.pl",
  "MathObjects.pl",
  "parserMultiAnswer.pl",
);

#####################################
#  Setup

Context("Numeric");
Context()->variables->are(
     r=>"Real",
     t=>"Real"
);

my $a=random(-3,3,1);           my $b=random(1,3,1);
my $r=non_zero_random(-3,3,1);

my @pow=([1,3,4],
         [2,2,3],
         [3,1,2]);
my $p=random(0,2,1);

my @soln=();  my @ok=(0,1,2,3,4,5,6,7,8);

for(my $i=0;$i<$pow[$p][0];$i++) {
  push @soln, Formula("(t^$i)*e^($a t)*cos($b t)")->reduce;
  push @soln, Formula("(t^$i)*e^($a t)*sin($b t)")->reduce;
}
for(my $i=0;$i<$pow[$p][1];$i++) {
  push @soln, Formula("t^$i")->reduce;
}
for(my $i=0;$i<$pow[$p][2];$i++) {
  push @soln, Formula("(t^$i)*e^($r t)")->reduce;
}

#############################
# answer evaluators

$ansSplice = sub {
   my ($correct, $student, $answerHash) = @_;   # get correct and student MathObjects
   my $context = Context()->copy;
   $context->flags->set(no_parameters=>0);
   $context->variables->add( c=>'Parameter' );
   my $c = Formula($context, 'c');
   for (my $i=0; $i<scalar(@ok); $i++) {
     if ( (Formula($context, "$c*$soln[$ok[$i]]") == Formula($context, "$student")) &&
          (Compute(0) != $student) ) {
       splice @ok,$i,1;
       return 1;
     }
   }
   return 0;
};


###########################
# problem text

$cxroot = Formula("r^2-2*$a*r+($a*$a+$b*$b)")->reduce;
$rroot = Formula("r-$r")->reduce;
$charEqn = Formula("($cxroot)^$pow[$p][0]r^$pow[$p][1]($rroot)^$pow[$p][2]")->reduce;

Context()->texStrings;
BEGIN_TEXT
A 9th order, linear, homogeneous, constant coefficient differential equation has
a characteristic equation which factors as follows.
\[ $charEqn = 0 \]
Write the nine fundamental solutions to the differential equation.
$PAR
\{ mbox( [
 "$SPACE \(y_1 = \)",
 ans_rule(10),
 "\(\qquad y_2 = \)",
 ans_rule(10),
 "\(\qquad y_3 = \)",
 ans_rule(10)
] ) \}
$PAR
\{ mbox( [
 "$SPACE \(y_4 = \)",
 ans_rule(10),
 "\(\qquad y_5 = \)",
 ans_rule(10),
 "\(\qquad y_6 = \)",
 ans_rule(10)
] ) \}
$PAR
\{ mbox( [
 "$SPACE \(y_7 = \)",
 ans_rule(10),
 "\(\qquad y_8 = \)",
 ans_rule(10),
 "\(\qquad y_9 = \)",
 ans_rule(10)
] ) \}
$PAR
(You can enter your answers in any order.)


END_TEXT
Context()->normalStrings;

$showPartialCorrectAnswer=1;

for(my $i=0; $i<9; $i++) {
  ANS( Formula("$soln[$i]")->cmp(checker => $ansSplice) );
}

ENDDOCUMENT();