| 微分方程组（dX）/（dt）=AX＋e^αtPm（t）具有重特征根α时的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^αtPm（t）具有重特征根α时的特解结构定理及应用[J].工科数学,2010(4):30-36. |
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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（2006207） |
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| 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.
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| 关 键 词： | 常系数非齐一阶线性微分方程组 特征根 特解 |
Structure Theorem of the Special Solution of the Differential Equation System（dX）/（dt）=AX＋e^αtPm（t） Which Having Repeated Characteristic Root and Its Application |
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| LIU Xu-cheng.Structure Theorem of the Special Solution of the Differential Equation System（dX）/（dt）=AX＋e^αtPm（t） Which Having Repeated Characteristic Root and Its Application[J].Journal of Mathematics For Technology,2010(4):30-36. |
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| Authors: | LIU Xu-cheng |
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| Institution: | LIU Xu-cheng (Department of Mathematics,Weifang University,Weifang,Shandong 261061,China) |
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| Abstract: | 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. |
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| Keywords: | the system of one order differential equations characteristic root special solution |
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