So while trying to model the physics of a rocket shot from the ground through the atmosphere, I came up with a second-order Non-Linear ODE of the form:
$$ \ddot y + \dot y^2 e^y = f(t) $$
This is simplified, of course, but I have been searching and cannot determine a solution or if there even IS an analytic solution. Of course, maybe from my short description of the problem you already see that I am taking the wrong approach entirely; if so, please direct me to the right line of thinking.
So in summary: Is there an analytic solution to this equation? If so, what is it? If not, how should I approach this problem given certain initial values to get a numeric solution?
Thanks very much in advance.