中文摘要：

二阶常系数线性非齐次方程是常微分方程中一类比较典型的方程,解的结构由齐次方程的通解与非齐次方程的特解构成。教材中求特解的做法是把非齐次项归纳为三大类,根据每一类的特点设定特解的基本形式,利用待定系数法寻找到特解。考虑到分类给教师教学与学生理解带来的麻烦,本文给出一种求此类方程特解的新方法,称之为待定函数法。利用此方法求特解可以不考虑非齐次项的具体形式,统一设定一个待定函数,通过求出这个函数得出非齐次方程的特解。

英文摘要：

Second-order linear nonhomogeneous differential equation with constant coefficients is a kind of typical equation in ODE. Its solution is combined by the general solution of the homogeneous differential equation and the particular solution of nonhomogeneous differential equation according to the structure of the non- homogeneous differential equations. The method of finding particular solution of nonhomogeneous differential equation is defined as following： classify the nonhomogeneous term into three cases firstly, then set the basic form based on the feature of each case, find the particular solution using the method of undetermined coefficients. Considering the trouble of teaching and understand of students derived by classification, we give a new method of finding particular solution of nonhomogeneous differential equation, called the method of undetermined functions. Using this method, we do not need consider the specific forms of nonhomogeneous terms and get the particular solution by setting an undetermined function.