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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 Name | Affiliation | | 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. |
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