Use Laplace transforms to solve the initial-value problem,

See figure(s) attached for my work.

I think I started this problem off correctly, however when it comes time to take the inverse laplace transform to obtain y(t) I think I may have taken the wrong route.

Should I be using partial fractions for this or is there another way? (We are a given a table of Laplace transforms that we can readily use without proof)

Let me know what you think.

Thanks again!