一类常系数非齐次线性微分方程特解的求法

A Particular Solution to the Kind of Non-homogeneous Linear Differential Equations with Constant Coefficients

针对n阶常系数非齐次线性做分方程y^(n)+p_1y^(n-1)+...+p_(n-1)y'+p_ny=e^(λx)(p_1(x)cosωx+p_m(x)sinωx),运用特征函数导数法和比较系数法,得到了方程的一个公式化特解,简单易行。

The eigenfunction derivative method and comparison coefifcient method can be applied to the n-order non-homogeneous linear differential equation with constant coefifcients, y（n）＋p1 y（n-1）＋…＋pn-1 y′＋pn y=eλx（p1（x）cosωx＋pm（x）sinωx）, and a formulable speciifc solution is obtained, which is simple and easy.