A pretty difficult problem about oscillatory circuit

[Sciencelad]

An oscillatory circuit

Homework Statement

So, there are parameters of a circuit. Also we got an answer. Just look at image below in the attachments.

Homework Equations

This problem uses simple differential equations. All I could write down here is on the wikipedia page: http://en.wikipedia.org/wiki/LC_circuit"

The Attempt at a Solution

After some pondering, I've got something about that.
$$\epsilon=L_{1}\frac{dI}{dt}$$
$$\epsilon_{c}=-L_{2}\frac{dI}{dt}$$
$$U=I*R$$
$$U\epsilon_{c}=\frac{q}{C}$$
So that:
$$IR+\frac{q}{c}=\frac{dI}{dt}(L_{1}-L_{2})$$

 

[Sciencelad]

http://img2.freeimagehosting.net/uploads/4475854ea8.gif