| 线性微分方程解函数线性无关的几种证法 |
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| 引用本文： | 胡博,王明建.线性微分方程解函数线性无关的几种证法[J].河南教育学院学报(自然科学版),2011(2):5-7. |
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| 作者姓名： | 胡博 王明建 |
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| 作者单位： | 河南工业大学理学院;郑州师范学院数学系 |
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| 摘 要： | 对于一般的常系数高阶线性微分方程,其解函数是否能构成方程的基本解组,需要证明其线性无关.利用行列式展开的直接法、高等代数中证明函数线性无关的定义法、算子法,并辅助反证法给出了详细的证明过程.
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| 关 键 词： | 常系数 高阶线性微分方程 解函数 基本解组 线性无关 算子 |
Some Methods of Linearly Independence of Solution on Linear Differential Equation |
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| HU Bo,WANG Ming-jian.Some Methods of Linearly Independence of Solution on Linear Differential Equation[J].Journal of Henan Education Institute(Natural Science Edition),2011(2):5-7. |
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| Authors: | HU Bo WANG Ming-jian |
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| Institution: | 1.College of Sciences,Henan University of Technology,Zhengzhou 450052,China;2.Department of Mathematics,Zhengzhou Normal University,Zhengzhou 450044,China) |
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| Abstract: | For higher-order linear ordinary differential equation,whether its solution function is fundamental system of equation’s solutions needs to prove the solution function’s linearly independence.By direct method of determinant expansion,definition method of linearly independence of functions in higher algebra,operator method,and assisting with proof by contradiction specifies the proof. |
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| Keywords: | constant coefficient higher-order linear differential equation solution function system of fundamental solutions linearly independence operator |
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