Complex ordinary differential equation
= Complex ordinary differential equation
{title2=$w'=A(z,w)$}
A first-order <ordinary differential equation> with complex independent and dependent variables is solved by a <holomorphic function> on an ordinary domain, and its <analytic continuation> can have <branch points>. A <holomorphic> right-hand side gives local existence and uniqueness by the integral <contraction mapping> used in the <Picard-Lindelöf theorem>.