I'm wondering if the following equation makes sense, and how to solve for

.

.

I found this equation when trying to solve the following problem :

http://www.physicshelpforum.com/phys...pacitance.html.

I wanted to find

. I realize the solution should be sinusoidal, so something like

.

Regarding the problem, when the capacitor halved its energy, I've found out that

. So I've found the boundary values and if I find

I'm done.

If I find

, I have that

and so I'm done.

I used Kirchhoff's law of voltage to find

. I might have done errors though.

Thank you for any help!