| 一类非线性微分方程的可积性 |
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| 引用本文： | 刘爱民,冯瑜,叶茂斌. 一类非线性微分方程的可积性[J]. 玉林师范学院学报, 2014, 0(2): 23-27 |
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| 作者姓名： | 刘爱民 冯瑜 叶茂斌 |
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| 作者单位： | [1]玉林师范学院教育技术中心,广西玉林537000 [2]玉林师范学院数学与信息科学学院,广西玉林537000 |
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| 基金项目： | 本工作受国家自然科学基金资助（11161051）. |
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| 摘 要： | 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．
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| 关 键 词： | 一阶非线性微分方程 可积性 Abel方程 Riccati方程 |
Integrability For a kind of Nonlinear DifFerential Equations |
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| LIU Ai-min,FENG Yu,YE Mao-bin. Integrability For a kind of Nonlinear DifFerential Equations[J]. Journal of Yulin Teachers College, 2014, 0(2): 23-27 |
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| Authors: | LIU Ai-min FENG Yu YE Mao-bin |
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| Affiliation: | 1. Education Technology Center, Yulin Normal University, Yulin, Guangxi 537000; 2. College of Mathematics ＆ Information Science, Yulin Normal University, Yulin, Guangxi 537000) |
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| Abstract: | 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 ofintegrability on two kinds of nonlinear differential equation are extended. Some known results are generalized. ） |
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| Keywords: | first nonlinear differential equation integrability Abel equation Riccati equation |
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