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Volume 8, Number 2, 2018, Pages 549-557                                                                DOI:10.11948/2018.549
On the equivalence of two differential equations by means of reflecting functions coinciding
Zhengxin Zhou and Yuexin Yan
Keywords:Reflecting function, reflecting integral, $\mu$-integral, equivalence, qualitative behavior.
      In this article, we discuss the equivalence of two differential systems by using the method of reflecting functions. We obtain some necessary and sufficient conditions under which certain differential equations are equivalent. Given these results, new types of differential systems equivalent to the given systems can be found. We also discussed the qualitative behavior of the periodic solutions of such differential systems. These results are new, in the sense that they generalize previous discussions on the equivalence of differential systems.
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