ODE Exact Equation Theorem

Theorem:

Given an ODE in the form of $M(x,y)dx+N(xy)dy=0$

If $\frac{\partial M}{\partial y}$ and $\frac{\partial N}{\partial x}$ are constants in x and y on an open set S,
then this ODE is exact on S iff $\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$

with the goal to find such an $F$