二阶线性非齐次微分方程的一个可积定理  

An integrable theorem of second order linear non-homogeneous differential equation

作　　者：张学元[1] 

机构地区：[1]湖南工程学院数理系,湖南湘潭411104

出　　处：《纺织高校基础科学学报》2004年第1期18-22,共5页Basic Sciences Journal of Textile Universities

摘　　要：研究在理论上和应用上占有重要地位的二阶线性非齐次微分方程的解法,引入特征方程组的概念,得到二阶变系数线性非齐次微分方程的一个新的、实用的可积充分判据,并给出了其通解的解析表达式,推广了经典的二阶常系数线性非齐次微分方程的解法.The solvable of second order linear non-homogeneous differential equation which in important in (theory) and practice is studied.The concept of characteristic equation system is leaded into second order linear differential equation.Thus a new practical integrable sufficient condition that variable coefficient second order linear non-homogeneous differential equation and analytic expression　fomula of the general solution is given.This extend the solution of classical constant coefficient second order linear non-homgeneous differential (equation).

关 键 词：二阶变系数线性非齐次微分方程 特征方程组 通解的解析表达式 

分 类 号：O175.1[理学—数学]