Movable singularity of a complex differential equation
= Movable singularity of a complex differential equation
= Movable singularities of a complex differential equation
{synonym}
A solution has a movable singularity if its location varies with the initial data. For example $w'=w^2$ has solutions $w=-1/(z-c)$, whose <pole> moves with $c$. The <Painlevé determinateness theorem> restricts movable singularities of first-order equations rational in the dependent variable to <poles> and <algebraic branch points>.