二阶线性微分方程的乘子可积性  

The Multipliers Integrability of Second Order Linear Differential Equation

作　　者：姬小龙[1] 高育晓[2] 刘卓军[1] 

机构地区：[1]中国科学院 数学机械化重点实验室,北京100080 [2]济源职业技术学院,河南济源454650

出　　处：《数学的实践与认识》2008年第4期161-166,共6页Mathematics in Practice and Theory

基　　金：中国科学院数学机械化重点实验室开放课题基金(KLMM07013)

摘　　要：在偏微分方程Riemann解法和微分方程裂变思想的启发下,引入了微分方程乘子函数(解)和乘子解法的概念,系统地讨论了二阶线性微分方程的乘子可积性.得到了二阶线性微分方程乘子可积的条件以及Riceati方程可积的充分必要条件,并分别给出了二阶线性微分方程和Riccati方程在乘子解下的通积分.Based on the numerical method of partial differential equation Riemann and the fission idea of differential equation, this paper introduces the concept of multipliers function and multipliers numerical method, discusses the multipliers integrability of second order linear differential equation by the numbers. It gains the multipliers integrable qualification of it, and receives the necessary and sufficient condition of Riccati＇s equation integrability, and thus obtains the general integral to second order linear differential equation and Riccati＇s equation in the multipliers solution separately.

关 键 词：二阶线性微分方程 乘子可积性 乘子解 RICCATI方程 

分 类 号：O175[理学—数学]