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

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.