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  

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

作　　者：徐千里[1] 

机构地区：[1]益阳师专数学系,益阳413049

出　　处：《数学理论与应用》2002年第2期89-93,共5页Mathematical Theory and Applications

摘　　要：本文利用等价方程组 ,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=acoset+ bsinet其中 P(D) =Dn + a1Dn-1+… + an,D=ddt,a1,a2 ,… ,an,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 .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.

关 键 词：常系数线性非齐次常微分方程 特解 友矩阵 JORDAN标准形 

分 类 号：O175[理学—数学]