求一类二阶非齐次欧拉方程的特解  

Special Solutions to A Kind of Second Order Non-homogeneous Euler Equations

作　　者：胡劲松[1] 

机构地区：[1]四川工业学院计算机科学与工程系,四川成都610039

出　　处：《重庆工学院学报》2003年第4期49-51,共3页Journal of Chongqing Institute of Technology

摘　　要：欧拉方程的解一般都是用"变量代换"法求得的,但是对于f(x)=Pn(x)eλx的这类欧拉方程而言,"变量代换"法求其特解相当困难。给出了这类方程为可积方程的一个充分条件,并用初等积分法[1]、[2]求出其特解。The solution to a Euler equation is always obtained with 'variable replacement' method. However, in terms of such kind of Euler equation as f(x)= Pn(x)eλx, a solution is difficult to be obtained with the 'variable replacement' method. This article presents a sufficient condition that makes this kind of equation integrable, and find the special solution with elementary integral.

关 键 词：特解 非齐次 二阶 欧拉方程 变量代换 初等积分 可积 困难 一般 充分条件 

分 类 号：O175[理学—数学] O241[理学—基础数学]