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

Structure Theorem of the Special Solution of the Differential Equation System(dX)/(dt)=AX+e^(αt)P_m(t) Which Having Repeated Characteristic Root and Its Application

作　　者：刘许成[1] 

机构地区：[1]潍坊学院数学系,山东潍坊261061

出　　处：《大学数学》2010年第4期30-36,共7页College Mathematics

基　　金：潍坊学院自然科学基金(2006207)

摘　　要：对于常系数非齐线性微分方程组(dX)/(dt)=AX+eαt sum (Bktk) from k=0 to m,当n级方阵A具有s≥1重特征根α时,本文给出了其特解X(t)的结构定理和计算方法,将求特解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X(t)的计算问题.For the system of one order linear inhomogeneous differential equations with constant coefficient （dX）/（dt）=AX＋eαt sum （Bktk） from k=0 to m,we give the structure theorem and the calculating method of its special solution when n order square matrix A has s≥1 repeated characteristic root.We turn the integral operation of seeking the special solution into the algebraic operation and solve the calculating problem of seeking special solution by computer.

关 键 词：常系数非齐一阶线性微分方程组 特征根 特解 

分 类 号：O175.1[理学—数学]