Exact equation

An equation $I(x,y)+J(x,y)D_x y=0 \Leftrightarrow I(x,y)dx+J(x,y)dy=0$ is exact iff $I_y=J_x$

. Then $\exists \psi (x,y)$ s.t.

$\begin{indisplay} \begin{aligned} & \psi _x (x,y)=I(x,y) \\ & \psi _y (x,y)=J(x,y) \end{aligned}\end{indisplay}$

and $\psi (x,y)=c$ is a solution.