Question

I am trying to solve a second order non-homogeneous differential equation where x(t) has u(t), the unit step as a part. i.e. x(t)=f(t)u(t)

I know how to 'guess' the particular solution for f(t) alone, but I'm not sure how it should be done when the unit step is appended.

Is there a standard method for guessing the particular solution in this scenario?

e.g. x(t)= Sin(3t)u(t), e^(-t)u(t),...