I have another RLC Circuit questions where L = 2.0H, R = 1.5 ohms and C = 0.2 F. The impressed voltage is E(t) = 20 sin 3t V.

I got a general solution for the D.E. as:

Using the initial conditions given ( Q(0) = 2.5C and I(0) = OA) I calculated the current as:

This just seems so messy. Can anyone help to confirm the answer or show me where I have gone wrong?