摘要
对著名的Riccati方程和二阶线性微分方程统一地引入了预解方程和预解常数的概念,导出了一系列新的实用的可积充分条件,推广了古典的和近代的可积性结果。文章还纠正了前人某些结果的错误。
This paper intrcduces two concepts of resolvent constant and resolvent equation into Riccati equation and Second order linear differential equation. Thus a series of new practical integrable sufficient conditions are derived and some classical and modern integrable results are extemded. This paper corrects some mistakes of the former's results, too.
关键词
RICCATI方程
二阶
线性微分方程
可积定理
Riccati equation, Second order linear differential equation, resolvent equation, resolvent constant, integrable, general solution
