The Particular Solutions for Certain Second Order Non-homogeneous Euler Equation

Based on variable transformation method, this paper deduces the linear ordinary differential equations with constant coefficients for some kinds of second order Euler equation x2y″+pxy′+qy=f(x). The particular solutions of special shape non-homogeneous terms f(x)=Axαcos(βln* are obtained by complex number algorithm, and the general formulas of scheme are given by *. The results of some examples illustrate the correctness of conclusion and practicality of the scheme presented．(* Indicates a formula, please see the full text)