Riccati型方程f'(y)dy/dx=P(x)f^2(y)+Q(x)f(y)+R(x)e^(∫Q(x)dx)的一个新的可积条件  

A New Condition of Integrability of Equation of Riccati Type f'(y)dy/dx=P(x)f^2(y)+Q(x)f(y)+R(x)e^(∫Q(x)dx)

作　　者：陈友朋 王英吉 罗思佳 CHEN Youpeng;WANG Yingji;and LUO Sijia(Mathematical School,Yancheng Normal Institute,Yancheng 224002,China)

机构地区：[1]盐城师范学院数学与统计学院,江苏盐城224002

出　　处：《高等数学研究》2018年第4期15-18,共4页Studies in College Mathematics

基　　金：江苏高校品牌专业建设工程资助项目(PPZY2015C211);盐城师范学院大学生实践创新项目

摘　　要：本文利用变量变换法与常数变易法给出Riccati型方程f'(y)dy/dx=P(x)f^2(y)+Q(x)f(y)+R(x)e^(∫Q(x)dx)的一个新的可积条件∫P(x)e^(∫Q(x)dx)dx=-1/2∫R(x)dx,同时给出该条件下方程的通解,并由此推得若干类Riccati方程的通解.Using the change of variable and the variation of constant,this paper gives a new condition of integrability f＇（y）dy/dx=P（x）f^2（y）＋Q（x）f（y）＋R（x）e^∫Q（x）dx,for the equation of Riccati type f＇（y）dy/dx=P（x）f-2（y）＋Q（x）f（y）＋R（x）e^∫Q（x）dx,and the general solution of the equation under the condition.Based on the approach,general solutions of several kinds of Riccati equations are also formulated.

关 键 词：RICCATI型方程 可积条件 通解 

分 类 号：O175.1[理学—数学]