常系数线性齐次微分方程的幂级数解

The Power Series Solution of Homogeneous Linear Ordinary Differential Equations with Constant Coefficients

级数法是求解常微分方程最有效的方法之一。给出了常系数线性齐次微分方程的仅与系数和初始值有关的幂级数解,对探究其它微分方程的幂级数解有一定的作用。

Method of series is one of the most effective approaches in seeking a solution of ordinary differential equations. In this pa-per I give the power series solutions of homogeneous linear ordinary differential equations with constant coefficients only related to the coefficients and the initial values.