一类指数型函数Riccati微分方程特解的存在条件及应用

Existence Conditions for Special Solutions to the Riccati Differential Equation of Exponential Functions and Their Applications

对于一类系数为指数型函数的Riccati微分方程y'=P(x)y2+Q(x)y+R(x),当P(x)、Q(x)和R(x)是指数型函数时,得到了此类方程特解存在的条件,并给出相关的应用.

We give a discussion of Riccati differential equation y＇ = P （x） y2 ＋ Q （x） y ＋ R （x） when P（x）,Q（x） and R（ x） are exponential type functions. The result obtained is the exist- ence conditions for special solutions to the equation. The related applications are also ad- dressed.