常系数线性非齐次微分方程求解的特征函数法

The Methods of Eigenfunction for Finding Solutions of Inhomogeneous Linear Differential Equation with Constant Cofficients

本文给出了五种求ｎ阶常系数线性非齐次微分方程待解的方法．这些方法只需计算特征函数Ａ（ｒ）及其各阶导数在某点的值，方法简单，两种递推公式适合计算饥计算，本文还简化了文［１］中递推公式（即本文的递推公式（二））的证明．

In this paper, we present five sorts of methods for finding the particular solutions of the n-th-order inhomogeneous linear differential equation with constant coefficients. These methods require only evaluating values of the eigenfunction A(r) and its all orders of derivative on some point.They are simple and two sorts of reeursion formulas are fit to compute with computer. Moreover the Proof of recursion formula in paper [1](namely recursion formula (two) in this paper) is simplified