玉林师范学院学报
玉林師範學院學報
옥림사범학원학보
Journal of Yulin Teachers College
2014年
2期
23-27
,共5页
一阶非线性微分方程%可积性%Abel方程%Riccati方程
一階非線性微分方程%可積性%Abel方程%Riccati方程
일계비선성미분방정%가적성%Abel방정%Riccati방정
first nonlinear differential equation%integrability%Abel equation%Riccati equation
基于分析技巧，讨论一类低阶非线性微分方程的可积性问题。将获的新结果应用于第一类Abel方程和Riccati方程，得到系统可积的一系列充分条件，推广了已有的相关结果。
基于分析技巧，討論一類低階非線性微分方程的可積性問題。將穫的新結果應用于第一類Abel方程和Riccati方程，得到繫統可積的一繫列充分條件，推廣瞭已有的相關結果。
기우분석기교，토론일류저계비선성미분방정적가적성문제。장획적신결과응용우제일류Abel방정화Riccati방정，득도계통가적적일계렬충분조건，추엄료이유적상관결과。
Based on the variation of constants, integrability for a kind of nonlinear differential equations is discussed. Moreover, the obtained results are applied to Abel equation and Riccati equation. A series of sufficient condition of integrability for Abel equation and Riccati equation are obtained. Therefore, the limits of integrability on two kinds of nonlinear differential equation are extended. Some known results are generalized.
