中心条件充分性的一些证明方法

Some Methods to Prove Sufficient Condition for a Critical Point to Be a Center

摘要: 在微分方程定性理论的学习中，中心充分条件的证明一直是热点以及难点，本文对中心充分条件的一些方法进行归纳总结，利用待定系数法求解积分因子及逆积分因子，解决了两类方程的可积性问题，利用变换的方法解决了一类方程的可积性问题。

Abstract: The sufficient condition for a critical point to be a center in planar qualitative theory has been a hot and difficult problem. Methods of proving the sufficient conditions are summarized, and the sufficiency of two systems was solved by using the method of undetermined coefficient to solve their integral factor and inverse integral factor. Finally, we prove the necessarily by using the transform method.