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)(adsbygoogle = window.adsbygoogle || []).push({});

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/(s^{2}+2^{2})] + [s/(s^{2}+2^{2})] - [2/s^{2}+2^{2}]

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!

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# Homework Help: Laplace Transforms

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