二阶常系数线性微分方程特解的微分算子法  

Differential operator method for particular solution for second-order constant coefficient linear differential equation

作　　者：李绍刚[1] 徐安农[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2008年第4期330-333,共4页Journal of Guilin University of Electronic Technology

摘　　要：微分算子法是求解常系数非齐次线性微分方程特解的有效方法,基于算子多项式的理论,针对二阶常系数线性微分方程,论文给出了非线性项为指数函数、三角函数、幂函数及其混合函数的微分算子特解公式,实例表明特解公式在解题中具有可应用性、有效性和简捷性。Differential operator method is an effective approach for solving inhomogeneous linear differential equation with constant coefficients. Based on the theory of operator polynomial and aiming at second order inhomogeneous linear differential equation with constant coefficients,differential operator particular solutions formula are given where the nonlinear item has several types of function such as exponential, trigonometry, power, mixture. The examples proved that the particular solution formula had the properties of application, validity and conciseness in solving problems.

关 键 词：线性微分方程 常系数 微分算子 特解 

分 类 号：O175.1[理学—数学]