I have the following equation
$$(xy^2 + x)dx + (yx^2 + y)dy=0$$ and I am told it is separable, but not knowing how that is, I went ahead and solved it using the Exact method.
Let $M = xy^2 + x $ and $N = yx^2 + y$
$$My = 2xy \text{ and } Nx = 2xy $$
$$ \int M.dx ==> \int xy^2 + x = x^2y^2 + (x^2)/2 + g(y)$$ $$ \text{Partial of } (x^2y^2 + (x^2)/2 + g(y)) => xy^2 + g(y)'$$ $$g(y)' = y$$ $$g(y) = y^2/2$$ the general solution then is $$C = x^2y^2/2 + x^2/2 + y^2/2$$
Is this solution the same I would get if I had taken the Separate Equations route?