一类高阶欧拉方程的通解  

General Solution of a Type of Higher Order Euler Equation

作　　者：邓瑞娟[1] 陈倩倩 DENG Rui-juan;CHEN Qian-qian(Basic Course Department,Wuhu Institute of Technology,Wuhu,241003,China)

机构地区：[1]芜湖职业技术学院基础部,安徽芜湖241003

出　　处：《红河学院学报》2021年第2期149-150,153,共3页Journal of Honghe University

基　　金：安徽高校自然科学研究重点项目(KJ2019A0976);安徽省高等学校质量工程项目(2017ghjc270)。

摘　　要：讨论了形如x^(n)y^((n))+p1x^(n-1)y(n-1)+p2x^(n-2)=x^(k)lnx的高阶欧拉方程。先针对二阶、三阶情形,通过运用经典的变量代换方法将变系数的欧拉方程变成常系数的线性方程,得到了的通解公式,并给出了应用实例;再将这一结果推广,得到了n阶情形的求解方法。In this paper,the higher order Euler equation of form is discussed.For the second and third order cases,the general solution formula is obtained by using the classical variable substitution method to change the Euler equation with variable coefficients into the linear equation with constant coefficients,and the application example is given.Then the result is extended to the solution method of the order case.

关 键 词：欧拉方程 常系数线性微分方程 变量替换 

分 类 号：O172.2[理学—数学]