微分方程组(dX)/(dt)=AX+e^(αt)(cosβt·P_m^((1))(t)+sinβt·P_m^((2))(t))具有重特征根α+iβ时的特解结构定理及应用

Structure Theorem of the Special Solution of the System of Differential Equations (dX)/(dt)=AX+e^(αt)(cosβt·P_m^((1))(t)+sinβt·P_m^((2))(t)) Which Has Repeated Eigenvalueα+iβ and Its Application

对于一阶常系数非齐线性微分方程组dX/dt=AX+eαt(cosβt.P(1)m(t)+sinβt.P(2)m(t)),P(1)m(t),P(2)m(t)为次数不超过m关于实变量t的n维向量实值多项式,当n级实方阵A具有s≥1重特征根α+iβ时,给出了其特解珟X(t)的结构定理和计算方法,使求特解珟X(t)的积分运算转化为简单的代数运算.解决了利用计算机求特解珟X(t)的计算问题.

For the system of fist-order linear inhomogeneous differential equations with constant coefficient dt/dx=AX＋e^αt（cosβt·Pm^（1）（t）＋sinβt·Pm^（2）（t））, we give the structure theorem and the calculating method of its special solution X（t） when n-order real matrix A has s-repeated eigenvalue α ＋ iβ, where Pm^（1） （t） and Pm^（2）（t） are n-dimension real-valued vector polynomial about real variahlet as well as their degrees are less than or equal to m. We turn the integral operation of seeking the special solution .X（t） into the algebraic operation and solve the calculating problem of seeking special solution.X（t） by computer.