You don't exactly write down the equation, but you write a piece of perl code that evaluates the equation.

If your system of equations is of this form:

f'(x) = x * y
g'(x) = x + y;
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You write in your program:

sub dydt {
   my ($t, $x, $y) = @_;
   return ($x * $y, $x + $y);
}
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And then proceed as the example in the docs shows.

Math::RungeKutta doesn't deal with symbolic equations, but expects you to do the evaluation instead.