I think I have a fair idea of how to solve my equations, using Laplace transform. But the partial fraction decomposition seems to elude me...

I get X and Y as such.

I get this:

I pulled the handbrake here because wolfram alpha got something else...

Wolfram Alpha, see: Partition fraction expansion

If anyone could find it in their heart to ease me throw this one, so that I can solve my system of differential equations...