This is the problem given:
I am not entirely sure what my Professor expected from an answer, but it seems I am to find the coefficient, angular frequency, and phase of the non-homogenous solution only. I know that the steady state means $\frac{dy}{dt}=0$, but how can I know the initial condition for $y$?
Using method of undetermined coefficients I got $y=c_1\exp\left(-\frac{2}{3}+\frac{\sqrt{19}}{3}\right)t+c_2\exp\left(-\frac{2}{3}-\frac{\sqrt{19}}{3}\right)-\frac{68}{353}\sin(2t)+\frac{32}{353}\cos(2t)$
for the solution.
Is the answer simply $A= \frac{32}{353},\, B=2,\, C=0?$
Also is this what the solution should look like?
4\cos(2t)">
The blue line is the solution y and the green dashed line is the signal $4cos(2t)$