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| 常系数非齐次线性微分方程特解的另一种求法 | |
| 引用本文： | 陈利娅,赖霞. 常系数非齐次线性微分方程特解的另一种求法[J]. 高等数学研究, 2010, 13(4): 75-77 |
| 作者姓名： | 陈利娅 赖霞 |
| 作者单位： | 西华大学数学与计算机学院,成都610039 |
| 摘 要： | 将常系数线性微分方程转化为一阶常系数线性微分方程组,并利用线性微分方程组的基解矩阵的性质和矩阵指数的性质以及非齐次线性微分方程组的常数变易公式,得到了常系数非齐次线性微分方程的积分形式的特解公式,并通过实例说明所得结论的有用性. |
| 关 键 词： | 常系数线性微分方程 线性微分方程组 特解 基解矩阵 矩阵指数 |
A Method to Find the Particular Solution of Nonhomogeneous LDE with Constant Coefficients |
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| CHEN Li Ya,LAI Xia. A Method to Find the Particular Solution of Nonhomogeneous LDE with Constant Coefficients[J]. Studies In College Mathematics, 2010, 13(4): 75-77 | |
| Authors: | CHEN Li Ya LAI Xia |
| Affiliation: | (School of Mathematics and Computer Engineering, Xihua University, Chengdu, 610039, PRC) |
| Abstract: | Based on properties of fundamental solution matrix, properties of matrix exponential function, and the method of variation of constant, a LDE with constant coefficient can be transformed into a system of first-order LDEs, thereby, a new particular solution formula turns up. Examples show that the new method works welt. |
| Keywords: | linear equation with constant coefficients system of linear equations special solution fundamental solution matrix matrix exponential function. |
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