Laplace ? Makes differentiation nothing more than linear equation which can be easily manipulated. Though the inverse Laplace maybe kind of tricky since you most likely will require partial fractions.
I have never coded anything like this in C, so these are just ideas I'm throwing out there. I guess it depends are your level of C programming.
If you can use Matlab, that would be the better way, since it's probably not as difficult as coding that type of equation in C.