关于一类一阶非线性微分方程封闭可积条件的一个注记  

A Note About Ciosed Integrability Conditions of First Order Nonlinear Diffrential Equation of the 1 st Kind

作　　者：冯录祥[1] 

机构地区：[1]石河子大学数学系,石河子832000

出　　处：《数学的实践与认识》2003年第4期110-117,共8页Mathematics in Practice and Theory

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.

关 键 词：非线性微分方程 封闭可积条件 初等解 RICCATI方程 Abei方程 

分 类 号：O175[理学—数学]