supported by Beijing Natural Science Foundation under Grant No.Z190004;the National Key Research and Development Project under Grant No.2020YFA0713703;the Fundamental Research Funds for the Central Universities.
Let f(t,y,y')=∑ _(i=0)^(n )a_(i)(t,y)y'^(i)=0 be an irreducible first order ordinary differential equation with polynomial coefficients.Eremenko in 1998 proved that there exists a constant C such that every rational ...