Im currently studying for a maths exam and im really stuck with part ii) of this question.
I have solved the homogenous equation i(x)=5cosx + 0sinx
would greatly appreciate someone walking me through part ii)
you need any solution for the inhomogeneous problem, because you have already solve the homogeneous ODE. For this reason an "ansatz" like does it. In this case you should use Eulers formula for the sin.
Edit: I guess, will totally work.
He is talking about the "method of undetermined coefficients". If you are expected to be able to solve a problem like this, you must have been taught that. It might be the complex exponential that is confusing you. I would recommend something like " " rather tham because your equation uses "sin(t)" rather than a complex exponential.
(Of course, .)
For part iii, that won't work because, with , " " and " " are already solutions to the associated homogeneous equation. Do you remember what to do in that case?