On the growth of certain meromorphic solutions of arbitrary second order algebraic differential equations

Abstract

In this note, we present two results concerning meromorphic functions on the whole finite plane, which are solutions of algebraic differential equations (i.e., equations of the form Ω ( z , y , d y / d z , ⋯ , d n y / d z n ) = 0 \Omega (z,y,dy/dz, \cdots ,{d^n}y/d{z^n}) = 0 , where Ω \Omega is a polynomial in z , y , d y / d z , ⋯ , d n y / d z n ) z,y,dy/dz, \cdots ,{d^n}y/d{z^n}) .