一类特殊Abel方程的可积条件

Integrable Condition to A Class of Special Abel Equation

通过分式线性变换u(x) =m(x)y(x) +n(x) (m(x) ,n(x) 为待定函数 ) ,将一类特殊Abel方程化为较简单的形式 ,由此判定了一些尚未解决的Abel方程的Liouville可积性 。

A class of special Abel equation can be simplified and its Liouville's integrability is validated by linear fractional transformation:u(x)=m(x)y(x)+n(x)(m(x),n(x)are uncertain functions).We can give some integrable condition about the special Abel equation.