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一类常微分方程的可积判据
引用本文:王金秀.一类常微分方程的可积判据[J].湖南文理学院学报(自然科学版),1999(4).
作者姓名:王金秀
作者单位:湖南纺织高等专科学校!湘潭,411104
摘    要:给出了一类非线性常微分方程的可积充分条件,它至少概括了一阶线性方程、Bernoulli方程等一些古典的可积类型,由它可导出Riccati方程和二阶线性方程的一系列新的、实用的可积性结果和可积类型。纠正了前人某些结果的错误。

关 键 词:常微分方程  可积  通解

The Integrable Criterion of a Sort of Ordinary Differential Equations
Wang Jinxiu.The Integrable Criterion of a Sort of Ordinary Differential Equations[J].Journal of Hunan University of Arts and Science:Natural Science Edition,1999(4).
Authors:Wang Jinxiu
Abstract:An integrable sufficient condition of a solt of nonlinear differential equations is proposed in this paper, which generalizes at least some classical integrable typpes, such as first - order linear equation. Bemoulli equahon. From it deriver a series of netw practical integrable resuls and types of foccati equation and second - order linear equation. Moreover, some mistakes in other re-searchers' results are pointed out and corrected.
Keywords:ordinary differential equation  integrable  general solution  
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