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微分方程组（dX）/（dt）=AX+eαt(cosβt·Pm（1）（t）+sinβt·Pm（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+eαt(cosβt·Pm（1）（t）+sinβt·Pm（2）（t）) Which Has Repeated Eigenvalueα+iβ and Its Application
【摘要】 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.
【Abstract】 For the system of fist-order linear inhomogeneous differential equations with constant coefficient dX dt=AX+eα t(cosβt·P(1)m(t)+sinβt·P(2)m(t)),we give the structure theorem and the calculating method of its special solutionX(t) when n-order real matrix A has s-repeated eigenvalue α+iβ,where P(1)m(t) and P(2)m(t) are n-dimension real-valued vector polynomial about real variablet as well as their degrees are less than or equal to m.We turn the integral operation of seeking the special solutionX(t) into the algebraic operation and solve the calculating problem of seeking special solution(t) by computer.
【Key words】 the system of fist-order linear inhomogeneous differential equations with constant coefficient； complex-valued function vector polynomial； special solution；
- 【文献出处】 大学数学 ,College Mathematics , 编辑部邮箱 ,2013年02期
- 【分类号】O175.1
- 【下载频次】55