On the Integrability and Equivalence of the Abel Equation and Some Polynomial Equations

Abstract

In this paper, first of all we give the necessary and sufficient conditions of the center of a class of planar quintic differential systems by using reflecting function method, and provide a simple proof of this results. Secondly, We use the reflecting integral to research the equivalence of the Abel equation and some complicated equations and derive their center conditions and discuss their integrability.