一类二阶常系数非齐次线性微分方程特解的矩阵方法

摘要

讨论二阶常系数非齐次线性微分方程yn+py'+qy=eλxpm(x)的特解，首先用待定系数法设出特解中的多项式，然后将多项式的系数满足的等式用矩阵方程表示，得到了求系数的一个新的公式解，可以简单地求出特解。%Discuss the particular solution of 2nd-order constant coefficient non-homogeneous linear differential equation yn+py'+qy=eλxpm(x) .At first suppose the polynomial in particular solution by using pending coefficients method,and then find the coefficients by solving the matrix equation they satisfied.So some new formulas are obtained,which simplify the course of finding the particular solution.