| 一类二阶时变系数线性微分方程的积分解 |
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| 引用本文： | 张学元.一类二阶时变系数线性微分方程的积分解[J].湖南工程学院学报(自然科学版),2003,13(4):88-94. |
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| 作者姓名： | 张学元 |
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| 作者单位： | 湖南工程学院,数理系,湖南,湘潭,411104 |
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| 摘 要： | 对一类二阶时变系数线性齐次微分方程和非齐次微分方程引入了特征方程的概念，给出了由其特征根确定通解和特解的积分表达式，推广了经典的二阶常系数线性微分方程和Euler方程的解法．
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| 关 键 词： | 二阶时变系数线性微分方程 特征方程 通解和特解的积分表达式 |
| 文章编号： | 1671-119X(2003)04-0088-07 |
| 修稿时间： | 2003年2月16日 |
Intergral Solution of One Kind Second Order Time Variable Coefficient Linear Difficiential Equation |
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| ZHANG Xue-yuan.Intergral Solution of One Kind Second Order Time Variable Coefficient Linear Difficiential Equation[J].Journal of Hunan Institute of Engineering(Natural Science Edition),2003,13(4):88-94. |
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| Authors: | ZHANG Xue-yuan |
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| Abstract: | In this paper,a concept of characteristic equation is introduced to one kind second order time variable coefticient linear homogeneous and non-homogeneous difficiential equation.The intergral expressions of general and special solution decided by its characteristic roots are given.Finally,the classic second order constant coefficient linear difficiential equation and an approach to Euler equation are extended. |
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| Keywords: | second order time variable coefficient linear difficiential equation characteristic equation intergral expressions of general and special solution |
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