A simple method to find out when an ordinary differential equation is separable

被引：3

作者：

Angel Cid, Jose ^{[1
]}

机构：

[1] Univ Jean, Dept Math, Campus Lagunilas,Ed B3, Jaen, Spain

来源：

INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY | 2009年 / 40卷 / 05期

关键词：

separation of variables; separable functions; first-order differential equations;

D O I：

10.1080/00207390802136578

中图分类号：

G40 [教育学];

学科分类号：

040101 ; 120403 ;

摘要：

We present an alternative method to that of Scott (D. Scott, When is an ordinary differential equation separable?, Amer. Math. Monthly 92 (1985), pp. 422-423) to teach the students how to discover whether a differential equation y' = f(x, y) is separable or not when the nonlinearity f(x, y) is not explicitly factorized. Our approach is completely elementary and provides a necessary and sufficient condition for separability, as well as simple formulas for the explicit factors of f(x, y).

引用

页码：659 / 662

页数：4