变系数微分方程的常系数化条件  

The Constant Coefficient Condition of Differential Equation with Variable Coefficient

作　　者：宋和平[1] 李军红[1] 崔宁[2] 

机构地区：[1]河北科技师范学院数理系,河北秦皇岛066004 [2]河北建筑工程学院教务处

出　　处：《河北科技师范学院学报》2006年第2期4-7,11,共5页Journal of Hebei Normal University of Science & Technology

摘　　要：不同于解具有e∫φ(z)dz形式的待定函数法,由引理1给出了n阶变系数微分方程具体的因变量代换形式,从而给出n阶变系数微分方程常系数化的充要条件并加以详细证明,由此得到二阶、三阶变系数线性微分方程常系数化的充要条件,同时指出三阶变系数微分方程在具体应用中令a1=0的简便性。对二阶变系数非线性微分方程的常系数化给出两个使其可积的条件,并举例论证。The constant coefficient condition of n differential equation with variable coefficient is given and expounded,the complexion of the second order and the third order is acquired,and the simplicity of third order differential equation with variable coefficient being applied with is pointed out as well.The two conditions of the second order nonlinear differential equation with variable coefficient are given and expounded with examples.

关 键 词：变系数方程 常系数化 变量代换 

分 类 号：O175[理学—数学]