Given $\frac{xdy+ydx}{x^2+y^2}$ I took partials of either coefficient wrt to other variable I get $\partial P/\partial y$ as $\frac{x^2-y^2}{(x^2+y^2)^2}$ and $\partial Q/\partial x$ as $\frac{-x^2+y^2}{(x^2+y^2)^2}$ and as these aren't equal it isnt exact.
However when i try find an integrating factor that is a only dependent on one of the variables i get a contradiction.
Can i just use inspection and say that $\frac{(x^2+y^2)}{xy}$ would work?