| 常系数齐次线性常微分方程的解 |
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| 引用本文： | 王五生. 常系数齐次线性常微分方程的解[J]. 河池学院学报, 2000, 0(2) |
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| 作者姓名： | 王五生 |
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| 作者单位： | 河池师专数学系!讲师广西宜州546300 |
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| 摘 要： | 本文首先证明了若当标准形矩阵有n个线性无关的循环向量 ,接着证明了常系数齐次线性常微分方程组存在m个与它的系数矩阵的m重特征根对应的线性无关的解。最后证明了常系数齐次线性常微分方程组存在n个线性无关的解 ,它的任一解可由这n个解线性表示
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| 关 键 词： | 微分方程组 若当标准形 重特征根 线性无关解 解空间 |
Solution of System of Homogeneous Linear Ordinary Differential Equations With Constant Coeffient |
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| Wang Wusheng. Solution of System of Homogeneous Linear Ordinary Differential Equations With Constant Coeffient[J]. Journal of Hechi University, 2000, 0(2) |
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| Authors: | Wang Wusheng |
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| Abstract: | This paper first proves that Jordan's canonical matrix of order n has n linearly independant cyclic vector, and then proves that system of homogeneous linear ordinary differential equations with constant coeffients has m linearly independant solutions which correspond to m-ple eginvalues of the coeffient matrix. Finally it proves that system of homogeneous linear ordinary differetial equations with constant coeffients has n linearly independant solutions and arbitrary solution is linear combination of the n slutions . |
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| Keywords: | system of differential equations Jordan's canonical matrix repeated eigenvalues linearly independant solutions solution space. |
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