A short note on the Painlevé XXV–Ermakov equation

Solutions of the second member of the Riccati chain and of the corresponding third order linear differential equation are related to solutions of the so-called Painlev é XXV–Ermakov equation via the Schwarzian derivative. The reduction to the generalized Ermakov equation is shown to arise naturally from the Painlevé XXV–Ermakov equation. Specifically, the first order system of ordinary differentia equations, equivalent to the Painlevé XXV–Ermakov equation, is analyzed by resolving points of indeterminacy of the vector field over P1 × P1.