二阶变系数线性微分方程与其对应的Riccati方程可积的等价性及应用  

Equivalence and Applications of Second Order Linear Differential Equations with Variable Coefficients and Integrability of Their Corresponding Riccati Equations

作　　者：张虹[1] 敏志奇[1] 

机构地区：[1]甘肃民族师范学院数学系,甘肃合作747000

出　　处：《甘肃联合大学学报（自然科学版）》2011年第3期22-23,39,共3页Journal of Gansu Lianhe University :Natural Sciences

摘　　要：揭示了二阶变系数线性非齐次微分方程与其对应的Riccati方程可积是等价的,二阶变系数线性齐次微分方程与其对应的Riccati方程可积是等价的,并给出了二阶变系数线性微分方程在其对应的Riccati方程有特解下的求解公式.The equivalence on Homogeneous and Non-homogeneous second order linear differential equations with variable coefficients and integrability of their corresponding Riccati equations was established.Furthermore,the formula of solution to second order linear differential equations with variable coefficients is given if their corresponding Riccati equation has special solutions

关 键 词：二阶变系数线性微分方程 RICCATI方程 特解 转化 

分 类 号：O175[理学—数学]