一阶常微分方程可积性研究的初等方法

On the Integrability of the First-order Ordinary Differential Equations

本文针对一类一阶常微分方程,给出基于变量代换和极坐标变换的求解一阶常微分方程通积分的初等方法,两种方法所得的结果完全一致,从而该方程的可积性可知.进一步地,基于通积分的显式表达式,我们分析获得该方程的全局轨道分布,得到经过退化平衡点的一族周期闭轨的存在性.

Using the methods including change of variables and polar coordinates,we study the integrability of a first-order ordinary differential equation.We show the global phase portrait of the associated planar autonomous system with degenerate singular point.