This extend the solutions of clossical constant coefficientlinear equation and the famous Euler equation and provide a effective method forsolving variable coefficient linear differential equation.

• 给出了具有指数型解的充要条件，推广了经典的常系数线性方程和著名的Euler方程的的解法，为求解变系数线性微分方程提供了有效的方法。