一类Riccati方程特解的探析  

Analysis of the special solutions of a class of Riccati equations

作　　者：赵临龙 ZHAO Linlong(School of Mathematics and Statistics,Ankang University,Ankang Shaanxi 725000)

机构地区：[1]安康学院数学与统计学院,陕西安康725000

出　　处：《首都师范大学学报（自然科学版）》2023年第6期8-11,共4页Journal of Capital Normal University：Natural Science Edition

基　　金：陕西省一流课程建设项目《常微分方程》(2020-156);陕西省科技厅研究项目(2022JM-050);2021年陕西省教育科学研究项目(SGH21Y021)。

摘　　要：Riccati方程在物理学和力学等学科有着广泛的应用,但由于Riccati方程存在的不可积性,使其求解异常困难。现利用Riccati方程的不变量关系,给出一类Riccati方程的解析解,使Riccati方程的不变量解法成为Riccati方程求解的重要路径。The Riccati equation is widely used in physics,mechanics and other disciplines,but due to the non integrability of Riccati equation,it is very difficult to solve it.In this paper,the analytic solution of a kind of Riccati equation is given by using the invariant relationship of Riccati equation,which makes the invariant solution of Riccati equation an important path to solve Riccati equation.

关 键 词：RICCATI方程 解析解 不变量 解法 

分 类 号：O175.2[理学—数学]