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
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
关键词
变系数线性非齐次微分方程
初等积分法
通解
Variable coefficient non-homogeneous linear differential equation
Integrability
General solution
Elementary integral method
