含有指数函数的Riccati微分方程通解的充要条件  

The Necessary and Sufficient Conditions of the General Solution of Riccati Differential Equation with Exponential Functions

作　　者：戴伟 叶永升[1] DAI Wei;YE Yongsheng(School of Mathematical Sciences,Huaibei Normal University,235000,Huaibei,Anhui,China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《淮北师范大学学报（自然科学版）》2020年第2期26-28,共3页Journal of Huaibei Normal University：Natural Sciences

基　　金：安徽省教育厅高等学校省级质量工程项目(2015mooc053,2015jxtd120,2017jxtd146,2016jyxm0932,2017jyxm0216,2017jyxm0214,2017kfk042);安徽省高校自然科学基金项目(KJ2016A633);淮北师范大学教学研究项目(jy2017105,jy2017111,jy2017127)。

摘　　要：Riccati微分方程一般没有初等解法,而当系数满足一定条件时,Riccati微分方程又是可解的.文章利用变量变换法讨论系数含有指数函数的Riccati微分方程通解存在的充分必要条件,为特殊类型的Riccati微分方程的求解提供一些思路,并给出它的应用.Riccati differential equation generally has no elementary solution.When the coefficients of Riccati differential equation satisfy certain conditions,it is solvable.In this paper,we discuss the necessary and sufficient conditions of the general solution of Riccati differential equation with exponential functions by using the methods of variable transformation.Some ideas are provided for solving some special Riccati differential equations and its application is given.

关 键 词：RICCATI微分方程 通解 指数函数 

分 类 号：O175[理学—数学]