一类一阶非线性微分方程封闭可积条件  

Closed Integrability Conditions of First Order Nonlinear Differential Fequation of the 1st Kind

作　　者：张孝理[1] 

机构地区：[1]株洲职业技术学院,湖南株洲412000

出　　处：《数学的实践与认识》2001年第6期740-749,共10页Mathematics in Practice and Theory

摘　　要：本文得到了较为广泛的一类一阶非线性微分方程的封闭可积充分条件 ,其实用性之一表现在著名的 Riccati方程和The conditions expressed by this paper is sufficient for first order nonlinear differential equation of the 1st kind to be closed integrability. One of the practicalities of the studies may be demonstrated by the fact that some of integrable solutions of the wellkown Riccati′s differential equation and Appel′s differential equation, both of classical and contempopary solutions, are characteristic ones deduced from closed integrability conditions which are concluded in this studies.

关 键 词：非线性微分方程 通解 封闭可积 充分条件 RICCATI方程 Appel方程 

分 类 号：O175.14[理学—数学]