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}) .