TY - JOUR T1 - On the Integrability and Equivalence of the Abel Equation and Some Polynomial Equations AU - Yan , Yuexin AU - Pan , Yingxin AU - Lu , Feifei AU - Zhou , Zhengxin JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 207 EP - 220 PY - 2021 DA - 2021/04 SN - 1 DO - http://doi.org/10.12150/jnma.2019.207 UR - https://global-sci.org/intro/article_detail/jnma/18858.html KW - Center condition, integrability, reflecting integral, equivalence. AB -

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.