求解常系数线性微分方程的代数方法  

An Algebraic Approach to Solve Linear Differential Equation with Constant Coefficients

作　　者：林开亮[1] 王兢[2] LIN Kai-liang;WANG Jing(School of Science Northwest A & T University,Yanglin 712100,Shaanxi,China;School of Science Minzu University of China,Beijing 100081,China)

机构地区：[1]西北农林科技大学理学院,陕西杨凌712100 [2]中央民族大学理学院,北京100081

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2019年第6期577-582,共6页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金数学天元基金(1182601057);中央高校基本科研业务费专项资金(Z109021708)

摘　　要：通过分析解非齐次的常系数线性微分方程的算子法的代数本质,建议一种纯代数的求解方法,对该方法的分析也引出了推导齐次方程通解的一个简便方法.该方法也适用求解齐次与非齐次的常系数线性递推关系(即差分方程).By demonstrating the algebraic essence of the operational calculus method for solving linear non-homogeneous differential equations with constant coefficients,we suggest a pure algebraic method for solving this kind of equations,from which derives a simplified method for getting the general solution of homogeneous equation.This method can also be used to solve homogeneous and non-homogeneous linear difference equations with constant coefficients.

关 键 词：求一术 算子法 微分方程 差分方程 

分 类 号：O211[理学—概率论与数理统计]