Second Order Differential Equation

[Axecutioner]

This is from an advanced college physics class, and I'm only in a Calc 1 right now. I've finished the whole problem except for this last part, which deals with a second order differential equation, which I don't know how to do yet.

Homework Statement

Givens: B, L, A, m, σ, θ (all are constant)
From what I have below, I need to get everything in terms of the givens, x, and t

Homework Equations

I have reduced everything down to this:
[PLAIN]http://img718.imageshack.us/img718/513/phy.png
The first equation is from the problem, the second gets it in differential equation form.

The Attempt at a Solution

Like I said above, I've solved the whole problem except what I haven't learned how to do yet.


Thanks!
~Axe

 

[vela]

Your differential equation isn't correct. It should be

$$\frac{B^2L^2\sigma A}{2L+2x}\frac{dx}{dt} = m\frac{dv}{dt} + mg \sin\theta$$

You can integrate that with respect to t to find v in terms of x and t. Is that what you're solving for?