Your answer can't be right because:
which is different from the original given .
If we proceed:
This means: , , and
Can you proceed?
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...