利用算子分解求解常系数非齐次线性微分方程  

Solving non-homogeneous linear differential equation with constant coefficients by operator-decomposition

作　　者：顾新丰 姚洪亮[1] GU Xin-feng;YAO Hong-liang(School of Science,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]南京理工大学理学院

出　　处：《高师理科学刊》2019年第7期1-4,共4页Journal of Science of Teachers＇College and University

基　　金：江苏省自然科学基金项目(BK20171421);南京理工大学高等教育教学改革研究项目(2017B22)

摘　　要：利用算子分解的方法给出了常系数非齐次线性微分方程的复通解.利用此通解,给出了特征根具有重数时齐次方程特解的形式,从而得到齐次方程的通解.给出了非齐次方程实的特解,从而得到了非齐次方程的通解.Uses the operator-decomposition method to give the complex general solution of non-homogeneous linear differential equation with constant coefficients.Uses this general solution to give the form of special solution of homogeneous equation when the multiple number of the characteristic root is nonzero,so that get the general solution of homogeneous equation.Gives the real special solution of non-homogeneous equation,so that get the general solution of non-homogeneous equation.

关 键 词：常系数非齐次线性微分方程 通解 特解 

分 类 号：O175.1[理学—数学]