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 DifferentialEquation with Variable Coefficients

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 self-variable transformation of unknown function, then a new soluable, type of second order linear differential equation with variable coefficients is obtained. Thus, the famous second order Euler equation is expanded.