Exact first-order ordinary differential equation
= Exact first-order ordinary differential equation
{title2=$F(x,y)=C$}
An equation $P(x,y)+Q(x,y)y'=0$ is exact if $P\,dx+Q\,dy$ 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.