常系数非齐次线性微分方程特解的新解法  

A New Method for Solving Special Solutions of Nonhomogeneous Linear Differential Equations with Constant Coefficients

作　　者：张辉 方晓峰 王静 ZHANG Hui;FANG Xiaofeng;WANG Jing(Department of Basic Courses,Rocket Force University of Engineering,Xi’an 710025,China)

机构地区：[1]火箭军工程大学基础部,陕西西安710025

出　　处：《河南教育学院学报（自然科学版）》2022年第4期39-43,共5页Journal of Henan Institute of Education(Natural Science Edition)

基　　金：陕西省教育厅教育教学课题重点项目(21BZ091);火箭军工程大学教育教学研究一般课题(HJJKTB2021027)。

摘　　要：研究了一种求解n阶常系数非齐次线性微分方程特解的方法——待定多项式法。基于自由项函数的两种情形分别给出了求解特解的思路方法和重要结论,并通过比较说明了此方法的优越性,旨在对常系数非齐次线性微分方程特解的求解有更深的理解和掌握。Studied a method,undetermined polynomial method,to solve the special solution of non-homogeneous linear differential equation with n-order constant coefficient.Based on two cases of free term function,gave the ideas,methods and important conclusions of solving the special solution,and illustrated the advantages of this method by comparison,so as to have a deeper understanding and mastery of the special solution of constant coefficient non-homogeneous linear differential equation.

关 键 词：线性微分方程 通解 特解 指数函数 多项式 特征方程 

分 类 号：O13[理学—数学]