一类新Riccati型方程的可积性及其应用

The Integrality of One Kind of New Riccati Equation and It's Application

对一类新Riccati型微分方程,在平凡情形下,证明了它是可积的;在非平凡情形下,给出了可积的一个实用的充分判据及其通解的表达式。作为应用,导出了一类新二阶变系数线性齐次微分方程的可积性。

In this paper,one kind of new Riccati differential equation is proved to be integrable in ordinary conditions. A practical sufficient integrable criterion and the expression formula of it's general solution in non-ordinary conditions are given .As it' s application, the integrality of one kind of new second-order variable confficient linear homogeneous differential equation is derived.