Abstract: Differential equation is of great importance in the advanced Mathematics. The solution method of second-order coefficient of linear differential equation is studied in general literature and textbooks, that is, undetermined coefficient method. The explanation of constant coefficient of linear differential equations to be determined index and non-homogeneous factor to be determined explanation is given, and a new method -- reduced order method is proposed and studied.

Key words: constant coefficient , linear , differential equation , undetermined coefficient method , characteristic equation , reduced order ;

摘要： 微分方程是高等数学重要内容之一,一般文献和教科书中仅研究到二阶常系数线性微分方程通解求法,方法 都是待定系数法。在这给出了常系数线性微分方程待定指数法和非齐次待定系数法的使用解释,研究和提出了一 种新的推导方法??降阶法。

关键词: 常系数, 线性, 微分方程, 待定系数法, 特征方程, 降阶