可化为变量分离方程的微分方程推广  

The generalization of variable separated differential equation

作　　者：陈翠玲[1] 何子群 韦莹[1] 黄秀文[1] 仇东雪 

机构地区：[1]广西师范大学数学与统计学院,广西桂林541004

出　　处：《高师理科学刊》2017年第3期6-8,共3页Journal of Science of Teachers＇College and University

基　　金：2016年广西自治区级大学生创新创业训练计划项目(201610602184);广西师范大学2015年教育教学改革立项项目(师政教学[2015]115号);2016年度广西高等教育本科教学改革工程项目(2016JGB163)

摘　　要：很多经典的一阶微分方程,如齐次微分方程和一阶线性微分方程,都是通过变量代换的方法转化为变量分离方程求解.将一些形式更为一般的一阶微分方程,通过适当的变形和变量代换,转化为变量分离微分方程,求出其通解,从而扩大可求解的微分方程的范围.It is well known that many classic first-order differential equations, such as the homogeneous differential equation, first order linear differential equation, is converted to variable separation equations through the method of variable substitution. Some more general first order differential equation is converted to the variable separated differential equation, through proper deformation and variable substitution, found out the general solution, thus further expand the scope of differential equation which can be solved.

关 键 词：变量代换 变量分离 微分方程 通解 

分 类 号：O175.1[理学—数学]