As some differential equation solving practise, I've been trying to derive the solution shown in a textbook on the left. Im trying to use ACos(wt)+BSin(wt) to solve for a particular solution, then later use Aexp^(Kt) later to solve for the homogeneous solution for the transient - is this the correct method? It's been a while since I've done these. However I'm already stuck and I'm not sure if I'm doing something wrong. I can already solve for the steady state response using phasors, but I'd like to try solving the differential this time and get in some much needed practise.

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Thanks!

Megamox