一类Riccati方程解法的研究及推广  

Research and Generalization of the Solution of a Class of Riccati Equation

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

机构地区：[1]安康学院数学与统计学院,陕西安康725000

出　　处：《山西师范大学学报（自然科学版）》2023年第3期4-8,共5页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：陕西省科技厅研究项目(2022JM-050);陕西省一流课程建设项目《常微分方程》(2020-156).

摘　　要：研究一类Riccati方程的可积性,给出其解法.通过变量求异方法,构造Riccati方程新变量的Bernoulli微分方程,间接求解Riccati方程.结果:对于无法表达成显式形式的Riccati方程给出隐式解以及给出隐式解存在的条件.将具体无法表达成显式形式的Riccati方程的求解,推广为一类Riccati方程求解的形式.Study the integrability of a type of Riccati equation and provide its solution.By using variable differentiation method,construct a Bernoulli differential equation with new variables in the Riccati equation,and indirectly solve the Riccati equation.For Riccati equations that cannot be expressed in explicit form,provide im-plicit solutions and provide the conditions for the existence of implicit solutions.Promote the solution of Riccati equations that cannot be expressed in explicit form to a class of Riccati equations the form of solution.

关 键 词：RICCATI方程 BERNOULLI方程 隐式解 间接求法 

分 类 号：O175.2[理学—数学]