Exact first-order ordinary differential equation ($F(x,y)=C$)

An equation $P(x,y)+Q(x,y)y^{\prime }=0$ is exact if $Pdx+Qdy$ is an exact differential form: there is a potential $F$ with $F_x=P$ and $F_y=Q$. Its solution curves are levels $F=C$. For continuously differentiable coefficients, $P_y=Q_x$ suffices locally and globally on a simply connected domain. Global topology matters; a closed form on a punctured domain need not be exact.