| 一类变系数线性微分方程及其解 |
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| 引用本文： | 尚德生.一类变系数线性微分方程及其解[J].大学数学,2009,25(3). |
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| 作者姓名： | 尚德生 |
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| 作者单位： | 山东理工大学,理学院,数学系,山东,淄博,255049 |
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| 基金项目： | 山东理工大学科研基金，学校博士启动基金 |
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| 摘 要： | 根据常系数线性微分方程的求解原理,通过一个适当变换,研究了一类变系数线性微分方程及其解的问题,从而可以得到这类方程在特征根都是互异单根时的解法和通解,并对三阶方程的各种情况进行了较为详尽的讨论.
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| 关 键 词： | 齐次线性微分方程 通解 变换 特征方程 |
A Kind of Linear Differential Equations with Variable Coefficents and Its Solutions |
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| SHANG De-sheng.A Kind of Linear Differential Equations with Variable Coefficents and Its Solutions[J].College Mathematics,2009,25(3). |
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| Authors: | SHANG De-sheng |
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| Institution: | Department of Mathematics;School of Science;Shandong University of Technology;Zibo;Shandong 255049;China |
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| Abstract: | A kind of linear differential equations with variable coefficients and the solutions are studied according to the method of solving the linear differential equations with ordinary coefficients,through a suitable transformation.And we obtained the general solutions of this kind differential equations when all the characteristic roots of the characteristic equation are simple,in the same time,we study all the cases of the third differential equations detailedly. |
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| Keywords: | linear differential equations general solutions transformation the characteristic equation |
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