一类二阶变系数线性微分方程的求解探讨  

Linear differential equations with variable coefficients

作　　者：陶筱平 TAO Xiao-ping(College of Mathematics and Statistics,Huanggang Normal University,Huanggang 438000,Hubei,China)

机构地区：[1]黄冈师范学院数学与统计学院,湖北黄冈438000

出　　处：《黄冈师范学院学报》2020年第6期42-46,共5页Journal of Huanggang Normal University

摘　　要：本文对系数为一次函数的二阶变系数线性微分方程是否有形如y=x^ke^rx类型的特解,以及求这种特解的方法进行了研究。首先证明了该类型方程的特解的充要条件,接着分析讨论了判断并求其特解的具体方法,还给出了通过特解y=x^ke^rx反向构造此类方程的一种方法,最后结合实例对定理的结论进行了验证。This paper focused on the second-order linear differential equations with variable coefficients,in which the variable coefficients were linear functions,and investigates whether such equations had a special solution of type y=x^ke^rx and the method of finding this special solution.First,the necessary and sufficient condition for the equation to have a special solution in the form of y=x^ke^rx was proved.Then the concrete method of judging and finding the special solution of type y=x^ke^rx was analyzed and discussed.Moreover,a method of constructing this kind of equation in reverse through the special solution of type y=x^ke^rx was given.Finally,examples were given to verify the conclusion of the theorem.

关 键 词：线性微分方程 变系数 一次函数 特解 

分 类 号：Q175[生物学—水生生物学]