| 一类二阶矩阵微分方程的特解 |
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| 引用本文： | 吴幼明,吴文峰.一类二阶矩阵微分方程的特解[J].四川理工学院学报(自然科学版),2012,25(6):61-64. |
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| 作者姓名： | 吴幼明 吴文峰 |
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| 作者单位： | 1. 佛山科学技术学院理学院,广东佛山,528000
2. 五邑大学数学与计算科学学院,广东江门,529020 |
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| 基金项目： | 国家自然科学基金资助项目，佛山科学技术学院创新团队项目 |
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| 摘 要： | 基于微分方程组理论和矩阵理论,采用按列比较方法和待定矩阵方法,给出了非齐次项为二次多项式与指数函数乘积的一类三维二阶常系数线性微分方程组的特解公式。对特殊情况进行了讨论,并通过算例验证了微分方程组特解公式的正确性。为高阶微分方程组的解法研究提供了一条有效的途径。
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| 关 键 词： | 微分方程组 待定矩阵法 按列比较法 |
Particular Solutions to One Kind of Second Order Matrix Differential Equation |
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| WU You-ming,WU Wen-feng.Particular Solutions to One Kind of Second Order Matrix Differential Equation[J].Journal of Sichuan University of Science & Engineering:Natural Science Editton,2012,25(6):61-64. |
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| Authors: | WU You-ming WU Wen-feng |
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| Institution: | 1.School of Science,Foshan University,Foshan 528000,China;2.School of Mathematics and Computation Science, Wuyi University,Jiangmen 529020,China) |
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| Abstract: | Based on differential equations theory and matrix theory,and by the method of column comparison and undermined matrix,the particular solution of a kind of three-dimensional second order differential equations with constant coefficients is obtained.And the non-homogeneous terms of differential equations are the form of quadratic polynomial multiplied by exponential function.The special cases are discussed in detail.For example,the particular solution formulas are validated.The research results have provided a foundation for the study of the method of solving on differential equations. |
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| Keywords: | differential equations method of undetermined matrix method of column comparison |
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