线性微分方程解函数线性无关的几种证法  

Some Methods of Linearly Independence of Solution on Linear Differential Equation

作　　者：胡博[1] 王明建[2] 

机构地区：[1]河南工业大学理学院,河南郑州450052 [2]郑州师范学院数学系,河南郑州450044

出　　处：《河南教育学院学报（自然科学版）》2011年第2期5-7,共3页Journal of Henan Institute of Education(Natural Science Edition)

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.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.

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 

分 类 号：O175.5[理学—数学]