| 微分方程组dX/dt=AX＋e~（αt）（cosβt·P_m~（（1））（t）＋sinβt·P_m~（（2））（t））特解结构定理及应用 |
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| 引用本文： | 刘许成.微分方程组dX/dt=AX＋e~（αt）（cosβt·P_m~（（1））（t）＋sinβt·P_m~（（2））（t））特解结构定理及应用[J].大学数学,2011,27(5):112-117. |
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| 作者姓名： | 刘许成 |
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| 作者单位： | 潍坊学院数学系,山东潍坊,261061 |
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| 基金项目： | 潍坊学院自然科学基金项目 |
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| 摘 要： | 对于一阶常系数非齐线性微分方程组dX/dt=AX＋e~（αt）（cosβt·P_m~（（1））（t）＋sinβt·P_m~（（2））（t））式中P（m1）（t）,P（m2）（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α＋iβ不是n级实方阵A的特征根时,本文给出了其特解~X（t）的结构定理和计算方法,使求特解...
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| 关 键 词： | 一阶常系数非齐线性微分方程组 复值函数向量多项式 函数矩阵 特解 |
Structure Theorem of the Special Solution of the System of Differential Equations dX/dt=AX＋e^at（cosβt·P^（1）m（t）＋sinβt·P^（2）m（t）） and Its Application ctt |
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| LIU Xu-cheng.Structure Theorem of the Special Solution of the System of Differential Equations dX/dt=AX＋e^at（cosβt·P^（1）m（t）＋sinβt·P^（2）m（t）） and Its Application ctt[J].College Mathematics,2011,27(5):112-117. |
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| Authors: | LIU Xu-cheng |
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| Institution: | LIU Xu-cheng(Department of Mathematics,Weifang University 261061,China) |
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| Abstract: | For the system of fist-order linear inhomogeneous differential equations with constant coefficient dX/dt=AX＋e^at（cosβt·P^（1）m（t）＋sinβt·P^（2）m（t））, we give the structure theorem and the calculating method of its special solution .X（t） when a＋ iβ is not the eigenvalue of n-order real matrix A, where P^（1） （t） and P^（2） （t） are n-dimension real-valued vector polynomial about real variablet as well as their degrees are less than or equal to rn. 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. |
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| Keywords: | the system of fist-order linear inhomogeneous differential equations with constant coefficient complex-valued function vector polynomial function matrix special solution |
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