一类Riccati方程特解的探析

Analysis of the special solutions of a class of Riccati equations

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.