二阶变系数线性微分方程的Riccati方程解法  

A Riccati Equation Approach to Second-order Linear Differential Equation with Variable Coefficients

作　　者：敏志奇[1] 

机构地区：[1]甘肃民族师范学院数学系,甘肃省合作市747000

出　　处：《曲阜师范大学学报（自然科学版）》2010年第4期57-60,共4页Journal of Qufu Normal University(Natural Science)

摘　　要：在(b′(x)b+2a(x)b(x))/b^2(x)≡c(常数)条件下,给出了微分方程y″+a(x)y′+b(x)y=f(x)(1)相对应的Riccati方程z′=z^2-a(x)z+b(x)(2)存在通解公式,进而得出了微分方程(1)或其齐次方程的通解公式.应用这些只与方程系数a(x)与b(x)相关的求解公式,求其通解过程十分简捷.This paper is concerned with the solving of second-order ordinary differential equation.Using the corresponding Riccati equation,the general solutions which relate the coefficients are established.

关 键 词：二阶变系数线性微分方程 RICCATI方程 通解 

分 类 号：O175.1[理学—数学]