...lar ordinary differential equation-不变流形的奇异常微分方程-知来数据 Key words: singular ordinary differential equation, stable manifold, center manifold, invariant manifold. [gap=420]关键词：奇异常微分方程，稳定流形，中心流形，不变流形。
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singular second-order ordinary differential equation 奇异二阶常微分方程
The ordinary differential equation singular boundary value problem is one of the most important branches of ordinary differential equations.
常微分方程边值问题是常微分方程理论研究中最为重要的课题之一。
The standard singular point is an important structure of the differential-algebraic equation systems(DAEs), by which DAEs are differentiated from the ordinary different equation systems (ODEs).
标准奇异点是微分代数方程系统区别于常微分方程系统的一个标志性的拓扑结构，具有重要的理论研究意义。
In this paper, some counter examples to the conclusions of singular solution and envelope in two textbooks of ordinary differential equation are given.
给出了两种常微分方程教材中关于奇解与包络关系结论的反例。
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