n阶变系数线性常微分方程的可积性  

The Integrability of the n-order Variable Coefficients Linear Ordinary Differential Equation

作　　者：胡爱莲[1] 郭俊[1] 

机构地区：[1]喀什师范学院数学系,新疆喀什844007

出　　处：《喀什师范学院学报》2009年第6期3-6,17,共5页Journal of Kashgar Teachers College

摘　　要：讨论了一类四阶、五阶变系数线性常微分方程的可积性,进而给出了方程y^((n))+a_1(x)y^((n-1))+a_2(x)y^((n-2))+…+a_(n-1)(x)y'+a_n(x)y=F(x)在条件下的初等积分法,并推出了其求解公式.Abstract：This paper considers the integrability of the class of fourth-order variable coefficient non-homogeneous linear differential equation, and deduces the integrability of the following equation and gives its the general solution formulas：y^（n）＋a1（x）y^（n-1）＋a2（x）y^（n-2）＋…＋an-1（x）y＇＋an（x）y=F（x）when the following conditions are satisfied {ana2＋ana＇1-a1a＇n=0 ana3＋ana＇2-a2a＇n=0 … … … anan-1＋ana＇n-2-an-1a＇n=0 a^2n＋ana＇n-1-an-1a＇n=0

关 键 词：变系数线性非齐次微分方程 初等积分法 通解 

分 类 号：O175.1[理学—数学]