A simple electrical circuit contains a condenser of capacity C farads, a coil of inductance L henrys, a resistance of R ohms, and a generator which produces an electromotive force E volts, in series. If the current intensity at time t at some point of the circuit is I amperes, the differential equation governing the current I is:

There is also a picture attached, not sure if its important so let me know.

Find I as a function of t if:

1. R=0, 1/(LC) = w^2, E= constant

2. R=0, 1/(LC) = w^2, E= Asin(alpha*t); alpha=constant≠w

3. R=0, 1/(LC) = w^2, E= Asin(wt)

4. R=50, L=5, C=9x10^-6, E= constant

If someone can just get me started, it would be much appreciated. I have utterly no clue what to do here