Ok, so I have uploaded/attached the question and the solution. I just need help understanding the solution please. I understand how to calculate the initial inverse transform, but I included it as the reference to the second part of the question regarding the y'' + 4y' = H(t-3) Can someone please explain the full steps to invert the laplace transform Y to f, like the solution shows in the last step? I have got to the following point, but I think I may be forgetting some Laplace Transform identities needed to make my life easier? I can split the equation into parts where I recognise a few Laplace Transforms but not sure about the rest, cheers... Y(s) = (1/s).e-3s.[1/(s2+22)] + [s/(s2+22)] - [2/s2+22] I recognise a few inverse laplace transforms there but without adding my confusion to the mess can someone please clarify how they got the answer? many thanks in advance. hopefully I didnt make this post toooo convoluted with my thoughts!