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重庆交通大学学报（自然科学版）

重庆交通大学学报（自然科学版） ›› 2009, Vol. 28 ›› Issue (1): 158-160.DOI: 10.3969/j.issn.1674-0696.2009.01.40

• • 上一篇    

常系数线性微分方程通解的另一种推导方法

陈春宝1,沈家骅2,丁颂康1   

  1. 1.上海海事大学文理学院,上海200135;2.上海海事大学数学与物理研究所,上海200135
  • 收稿日期:2008-07-22 修回日期:2008-07-27 出版日期:2009-02-15 发布日期:2015-04-15
  • 作者简介:陈春宝(1965—),男,江苏江阴人,讲师,主要从事数学教学和研究方面的工作。

A New Solution of Linear Differential Equations with Constant Coefficient

CHEN Chun-bao1,SHEN Jia-hua2,DING Song-kang1   

  1. 1. School of Arts ＆ Science, Shanghai Maritime University, Shanghai 200135, China; 2. Institute of Mathematics ＆ Physics, Shanghai Maritime University, Shanghai 200135, China
  • Received:2008-07-22 Revised:2008-07-27 Online:2009-02-15 Published:2015-04-15

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摘要： 微分方程是高等数学重要内容之一,一般文献和教科书中仅研究到二阶常系数线性微分方程通解求法,方法 都是待定系数法。在这给出了常系数线性微分方程待定指数法和非齐次待定系数法的使用解释,研究和提出了一 种新的推导方法??降阶法。

关键词: 常系数, 线性, 微分方程, 待定系数法, 特征方程, 降阶

Abstract: Differential equation is of great importance in the advanced Mathematics. The solution method of second-order coefficient of linear differential equation is studied in general literature and textbooks, that is, undetermined coefficient method. The explanation of constant coefficient of linear differential equations to be determined index and non-homogeneous factor to be determined explanation is given, and a new method -- reduced order method is proposed and studied.

Key words: constant coefficient , linear , differential equation , undetermined coefficient method , characteristic equation , reduced order ;

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