关于伯努利方程的解法探讨  

Discussion on General Solutions of Bernoulli Ordinary Differential Equation

作　　者：张玮玮 陈定元 ZHAN GWeiwei;CHEN Dingyuan(School of Mathematics and Computation Science,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数学与计算科学学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2018年第3期94-95,共2页Journal of Anqing Normal University(Natural Science Edition)

基　　金：安徽省高等学校省级教学研究项目(2015jyxm230);安庆师范大学数学学院教研项目(AQSX2016003)

摘　　要：伯努利方程是一类特殊的一阶非线性常微分方程。关于伯努利方程通解的求法众多,但仍是一个开放的课题。本文结合伯努利方程的结构特点,先猜想了一种新的通解形式,然后论证其正确性,最后,通过具体实例说明该方法的有效性。The Bernoulli ordinary differential equation is a special one order nonlinear ordinary differential equations.There exist some methods on solving the Bernoulli equation,however,solving the general solution is still an open topic.In this paper,according to the structural characteristics of the Bernoulli ordinary differential equation,a new general solution is conjectured.Then,the result is proofed.Finally,an example is given to illustrate the effectiveness.

关 键 词：伯努利方程 通解 非线性常微分方程 积分 

分 类 号：O175.1[理学—数学]