How to solve this ODE?
$$(1+xy) y\,dx + (1-xy)x\,dy = 0$$
We have been taught only these 3 types of problems: separable, linear equations or homogeneous. I tried using these methods, but I don't think this is a homogeneous or a linear differential equation. I tried separating the variables but couldn't. I strongly believe that this can be only solved by separating variables otherwise the question is wrong.