| 关于一类一阶非线性微分方程封闭可积条件的一个注记 |
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| 引用本文： | 冯录祥.关于一类一阶非线性微分方程封闭可积条件的一个注记[J].数学的实践与认识,2003,33(4):110-117. |
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| 作者姓名： | 冯录祥 |
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| 作者单位： | 石河子大学数学系,石河子,832000 |
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| 摘 要： | 给出了一类一阶非线性微分方程y′=p( x) y +q( x) yμ +r( x) +∑ni =2fi( x) yi较为广泛的一个封闭可积条件 ,它推广和统一了文献 1]中的定理 1和定理 2 ,特别指出近年来关于著名Riccati方程和 Abei方程可积性的一批最新结果都是它的特例
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| 关 键 词： | 一阶非线性微分方程 Riccati方程 Abei方程 可积 初等解 |
| 修稿时间： | 2002年3月8日 |
A Note About Ciosed Integrability Conditions of First Order Nonlinear Diffrential Equation of the 1st Kind |
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| FENG LU- xiang.A Note About Ciosed Integrability Conditions of First Order Nonlinear Diffrential Equation of the 1st Kind[J].Mathematics in Practice and Theory,2003,33(4):110-117. |
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| Authors: | FENG LU- xiang |
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| Abstract: | The by this paper is sufficient for first order nonlinear differential equation of the 1 stkind y′=p(x) y +q(x) yμ+r(x) +∑n i=2 fi(x) yi to be closed integrability.The resultobtained generalize and unify theorem1 and theorem2 in the literature 1 ] ,and explains that some latest results of integrable for wellkown Abel equation and Riccati rquation are special cases of its outcome. |
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| Keywords: | firsts order nonlinear differential equation Abel equation Riccati equation integrability elementary solution |
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