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What I've got so far is:

x'' + w^2x = Fsinwt --> x(homogenous) = Acoswt + Bsinwt

I know I have to find a particular solution but I keep getting zero as a result which I know won't solve the ODE.

Also, I know that the answer is (F/2w^2)sinwt - (F/2w)tcoswt