Given:

y'' +4y = sin3t

y'(0) = y(0) = 0

From this, I can pretty easily find Y(s) to be:

Y(s) = 3/[(s^2 + 3^2) (s^2 + 2^2)]

In the above, I can see sin3t and (1/2) sin2t, but I'm having trouble seeing how to get back to just plain y(t). Any help will be appreciated.