一类多项式系数二阶线性微分方程解法的研究  

The Study of the Solutions for a Second Order Linear Differential Equation with Polynomial Coefficients

作　　者：胡亦郑[1] 李素梅[2] 罗勇[1] 

机构地区：[1]温州大学数学与信息科学学院,浙江温州325035 [2]西安交通大学数学与统计学院,西安710049

出　　处：《大学数学》2015年第3期27-33,共7页College Mathematics

基　　金：浙江省教育厅项目(Y2013127178)

摘　　要：给出了一类具有多项式系数的二阶线性微分方程有多项式型特解和通解的充要条件,并在Maple下实现了这类微分方程具有多项式型特解和通解自动判定和求解的算法.The sufficient and necessary condition that there exists the polynomial particular solutions and the generalized solutions of a second order linear differential equation with polynomial coefficients is given. And it is realized to automatically determine whether the second order linear differential equation with polynomial coefficients has polynomial particular solutions and the generalized solutions and to automatically solve the polynomial particular solutions and the generalized solutions in Maple.

关 键 词：多项式系数 多项式型特解 算法实现 

分 类 号：O175.1[理学—数学]