Solve the initial value problem:
$x^2 + 2xy -y^2 = (2xy - x^2 + e^y)y'$
Answer the question with the relation y as a function of x.
I've been working on the following question and can't quite seem to figure out what to do. I understand that this is a Non-linear first-order ODE, and I think that it might be separable. The thing is I don't quite know how to solve this if it is separable. I thought that maybe the first step is to divide, so it becomes:
$(x^2 + 2xy -y^2)\div(2xy - x^2 + e^y) = y'$
I'm not quite sure how to get it in the following form: $dy/dx = f(x)g(y)$ (form for seperable ODE)
Any help with this would be much appreciated.