DOCUMENT() ;        

loadMacros(
   "PGstandard.pl",
   "MathObjects.pl",
   "PGML.pl"
);

Context("Numeric");
Context()->variables->add(a => 'Parameter');
Context()->variables->add(b => 'Parameter');
Context()->variables->add(t => 'Real');

# roots of the characteristic equation
$r1 = -1;
$r2 = -3;

$a = -($r1+$r2);
$b = $r1*$r2;

# elements of the target function
$c = -19;
$d = 4;
# Looking for this particular solution:
#  (-0.542857*t+0.186122)*e^(4*t)

$den = ($d)**2 + $d*$a + $b;
$A = $c/$den;
$B = -($A * (2*$d + $a))/ $den;

$yh = Formula("a*e^($r1*t) + b*e^($r2*t)")->reduce;
$yp = Formula("($A * t + $B) * e^($d*t) ");
$ans = $yp+$yh;  # Using this line, correct answer $yp is rejected.

TEXT(beginproblem()) ;
BEGIN_PGML


DEBUG: r1=[$r1], r2=[$r2], c=[$c], d=[$d].

Find a particular solution to 

[``\qquad y'' + [$a]y' + [$b]y =  [$c]t e^{[$d]t} . ``]

ANSWER: [`\quad y_{p}(t) =\  `][__________________________________________________]{$ans}

END_PGML
ENDDOCUMENT() ;