Rational Solutions of First Order Algebraic Ordinary Differential Equations

Ruyong Feng, Shuang Feng

Let $f(t,y,y^{\prime })={\sum }_{i=0}^d{a}_i(t,y)y^{\prime i}=0$ be a first order ordinary differential equation with polynomial coefficients. Eremenko in 1999 proved that there exists a constant $C$…