n阶常系数线性非齐次常微分方程P（D）x=acose^t＋bsine^t的特解

本利用等价方程组，友矩阵与Jordan标准型，研究了n阶常系数线性非齐次常微分方程P（D）x=acose^t bsine^t其中P（D）=D^n a1D^n-1 … an,D=1/dt,a1,a2,…a,a,b为任意实常数，在友矩阵具有n个不同的特征根的条件下，给出了求上述方程的特解的方法，最后给出一个详细的实例。

A Particular Solution of a Nonhomogeneous nth Order Linear Ordinary Differential Equations P(D)x=acose~t+bsine~t with Constant Coefficients

This paper is devoted to the study of a nonhomogeneours nth order linear ordinary differential equations with constant coefficients P(D)x=acose t+bsine t Where P(D)=D n+a 1D n-1+...+a n,D=SX(ddtSX),a 1,a 2,...,a n,a,b are arbitrary real constants.By using equivalent system,companion matrix,and Jordan Canonical form,for the Case in which the Companion matrix has n distinc eigenvalues,a method of finding a particular solution to the above equation is obtained.A illustrative example is presented in detail at the end of this paper.