用函数变换法求解二阶欧拉方程  

Solving Euler Equation of 2-Order by the Method of Function Transformation

作　　者：晏力[1] 胡劲松[1] 

机构地区：[1]西华大学数学与计算机学院,四川成都610039

出　　处：《西昌学院学报（自然科学版）》2008年第2期36-38,共3页Journal of Xichang University(Natural Science Edition)

摘　　要：通过"函数变换"将二阶欧拉方程降阶为可积的一阶线性微分方程,从而得到其积分形式的通解,还得到了一类非齐次欧拉方程特解的简单公式。该方法比用"自变量代换"法将欧拉方程转化为常系数线性微分方程进而求其解的过程更简单、更直接。By the methods of function transformation, non-homogeneous linear differential equations of constant coefficient of 2-order are reduced into integrable linear differential equations of 1-order. It obtains special solution of a kind of special differential equations. This method is more simple and direct than variable replacement method to make Euler equation transform linear differential equation of constant coefficient.

关 键 词：函数变换法 欧拉方程 通解 

分 类 号：O241.8[理学—计算数学]