How do I solve this differential equation $yy'=Ax+Byx^2$?
I have tried so many times but it seems that it is not the type which has been introduced in any textbook about differential equation. An approximate solution is also acceptable if it doesn't have closed-form solution.
This differential equation does not appear to have closed-form solutions. Are you sure the question asks you to solve it?
EDIT: Maple calls this an Abel equation of the second kind, class A. These do not have closed form solutions in general. In particular, Maple, finds no symmetries for your equation.