变量变换和几类里卡提方程的通解  

Transformation Method and the General Solution of Nonlinear Riccati Differential Equation

作　　者：倪华[1] 刘向旭 孙菲 NI Hua;LIU Xiang-xue;SUN Fei(Faculty of Science,Jiangsu University,Zhenjiang Jiangsu 212013,China)

机构地区：[1]江苏大学理学院,江苏镇江212013

出　　处：《大学数学》2019年第2期99-105,共7页College Mathematics

基　　金：江苏大学高级人才基金资助项目(14JDG176);江苏大学第16批大学生科研立项(Y16A098)

摘　　要：研究了几类里卡提方程,利用变量变换法将其化为伯努利方程或可分离变量微分方程,从而求出方程的通解,还得到方程的一个特解.并给出了几个例子来验证主要结论.Several kinds of Riccati equation are studied,which can be transformed into Bernoulli equation or separable variable differential equation by variable transformation method.The general solution of the equation and a special solution of the equation are obtained.Several examples are given to verify the main conclusions.

关 键 词：里卡提方程 变量变换法 通解 

分 类 号：O175.14[理学—数学]