RLC Low-Pass Circuit: Find Current in Resistor

[FermatPell]

Homework Statement

Find the current through the resistor in the following RLC low-pass circuit:

(there's an EMF missing on the left side, V=Vo cos(omega*t)

Homework Equations

Kirchoff's loop rule

The Attempt at a Solution

By using Kirchoff's loop rule and the junction rule, i get two differential equations. But I am stuck, can't solve them.

 

[rude man]

By using Kirchoff's loop rule and the junction rule, i get two differential equations. But I am stuck, can't solve them.

Show them why don't you ...