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On the Integrability and Equivalence of the AbelEquation and Some Polynomial Equations
  
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KeyWord:Center condition, integrability, reflecting integral, equivalence
Author NameAffiliation
Yuexin Yan Guangling College, Yangzhou University, Yangzhou, Jiangsu 225009, China 
Yingxin Pan Department of Mathematics and Physics, Nantong Teachers College, Nan- tong, Jiangsu 226006, China 
Feifei Lu School of Mathematical Sciences, Yangzhou University, Yangzhou, Jiangsu 225009, China 
Zhengxin Zhou School of Mathematical Sciences, Yangzhou University, Yangzhou, Jiangsu 225009, China 
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Abstract:
      In this paper, first of all we give the necessary and sufficient con- ditions of the center of a class of planar quintic differential systems by using reflecting function method, and provide a simple proof of this results. Sec- ondly, 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.