多项式系数三阶齐次线性微分方程的解法  

Solution of Third Order Homogeneous Linear Differential Equation with Polynomial Coefficients

作　　者：李思铭 姜永[1] LI Siming;JIANG Yong(College of Computer and Information,Fujian Agriculture and Forestry University,Fuzhou 350002,China;College of Mathematical Sciences,Dalian University of Technology,Dalian Liaoning 116024,China)

机构地区：[1]福建农林大学计算机与信息学院,福州350002 [2]大连理工大学数学科学学院,辽宁大连116024

出　　处：《大学数学》2023年第1期13-19,共7页College Mathematics

基　　金：福建省大学生创新创业训练项目(S202010389080);福建农林大学数学建模实训室项目(111ZS1503)。

摘　　要：针对一类具有多项式系数的三阶齐次线性微分方程的多项式型解展开研究,基于齐次线性方程组有非零解的充分必要条件给出该类方程存在多项式特解和通解的充要条件,设计相应算法和例子,并通过MATLAB数学软件实现判断该类方程是否存在多项式解以及求多项式型解的目的.We study the polynomial solution of a class of third-order homogeneous linear differential equations with polynomial coefficients.Based on algebraic theory,we give the necessary and sufficient conditions for the existence of polynomial special solution and general solution of this class of equations and design corresponding algorithms and examples.The purpose of judging the existence of polynomial solution and finding polynomial solution of this class of equations is realized by MATLAB mathematical software.

关 键 词：多项式系数 三阶线性微分方程 多项式解 MATLAB 算法 

分 类 号：O175.1[理学—数学]