My first DiffEq exam was yesterday and one of the questions we had in that exam was this:

$$ (2xy \; + \; 2x)dx \; -ydy =0 $$

What I did was I multiplied $dx$ by both terms in between the brackets, then took: $$ 2xdx \; -ydy = 0 $$ and solved it as: $$ x^2 - \; \frac {y^2}2 = C $$
then solved the first term $ \int 2xy \; dx $ and in the end I got: $$ x^2y + x^2 - \frac {y^2}2 = C $$

is this correct?

Thanks!