I'm interested in coming up with an function that approximates the solution to a non-linear differential equation. (There is no known closed form solution) The equation is Y''=(1/Y)(Y')^2-Y*A+Y^2*A where "A" is a constant, and Y' and Y'' are the first and second derivatives with respect to x. How would I look for approximations to the answer in the literature? Is this equation a member of a certain class of differential equations? Is there a technique known to work well? Any help would be appreciated!