first of all I'm not a mathematician, so I apologize if any of my understanding and terminology isn't up to par. Also, I've never used this website (or any of these kind of question/answer) websites before, hope it works.

I'm a mech. eng having trouble with a differential equation that is crucial to my research in graduate school. I've spend a long time trying to look up and understand tons of sources anything from books to buddies around the college.

This is the differential equation:

$$\dfrac{F(t)}{\left(\frac{dy(x)}{dx}\right)^2+1}=c^2y^2\left(\frac{d^2x(t)}{dt^2}\right)^2$$

I'm trying to solve for y which I THINK is dependent on x only, but i'm not sure. It could be y(x) or y(t). I also think this is a 1st order non-linear non-homogenous DE, but again I'm not sure. I initially thought it might be a partial differential equation though.

Any help would be greatly appreciated!

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Try rewriting $\frac{dy}{dx}$ as $\frac{dy}{dt}\frac{dt}{dx}$. – Donkey_2009 Jul 18 '13 at 10:56
I think you should clarify a little bit: Do you want to find $y(x)$, $x(t)$ or $y(x(t))$? – whatever Jul 23 '13 at 21:43