Use the Laplace transform to solve the initial value problem.

$\displaystyle y''-2y'+2y=cos t, y(0)=1, y'(0)=0$

Ok, so after doing the Laplace of both sides I am getting that $\displaystyle Y(s)=s-2+(s/s^2+1)/s^2-2s+2$

I am pretty sure that is correct but you may want to check me on that. Anyways, I am not sure what Y(s) becomes after this. Can someone help please?