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.
出处
《数学的实践与认识》
CSCD
北大核心
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)
关键词
二阶线性微分方程
乘子可积性
乘子解
RICCATI方程
second order linear differential equation
multipliers integrability
multipliers solution
riccati＇s equation
