Rational Solutions of First Order Algebraic Ordinary Differential Equations

Shuang Feng, Li-Yong Shen

Let $f(t,y,y^{\prime })={\sum }_{i=0}^n{a}_i(t,y)y^{\prime i}=0$ be an irreducible first order ordinary differential equation with polynomial coefficients. Eremenko in 1998 proved that there exists a c…