变系数二阶线性微分方程的一个新的可解类型  

A New Solvable Type of Second Order Linear Differential Equation with Variable Coefficients

作　　者：胡爱莲[1] 宋爱丽[1] 

机构地区：[1]喀什师范学院数学系,新疆喀什844000

出　　处：《河南科学》2008年第11期1296-1298,共3页Henan Science

基　　金：新疆维吾尔自治区高校科研计划重点项目(XJEDU2006165);喀什师范学院校内课题

摘　　要：通过双变换——未知函数的线性变换和自变量变换,将一类变系数线性微分方程化为二阶常系数线性微分方程,从而得到变系数二阶线性微分方程的一个新的可解类型,推广了著名的二阶Euler方程.In this paper, a kind of linear differential equation with variable coefficients is turned into second order linear differential equation with constant coefficients through double transformation--linear and serf-variable transformation of unknown function, then a new solvable type of second order linear differential equation with variable coefficients is obtained. Thus, the famous second order Euler equation is expanded.

关 键 词：变系数二阶线性微分方程 双变换 新的可解类型 通解 

分 类 号：O175.1[理学—数学]