Geodesic
On the order of growth of transcendental entire solutions of algebraic differential equations of second order
Sbornik. Mathematics, Tome 14 (1971) no. 2, pp. 281-296

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The basic result is the following. Theorem. A differential equation of the form $P(z,y,y',y'')=0$, where $P(z,u,v,w)$ is a polynomial in the variables $z$, $u$, $v$ and $w$, cannot be satisfied by entire transcendental functions of zero order of growth. Figures: 1. Bibliography: 10 titles. 
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     title = {On the order of growth of transcendental entire solutions of algebraic differential equations of second order},
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V. V. Zimoglyad. On the order of growth of transcendental entire solutions of algebraic differential equations of second order. Sbornik. Mathematics, Tome 14 (1971) no. 2, pp. 281-296. http://geodesic.mathdoc.fr/item/SM_1971_14_2_a7/