On transcendental meromorphic solutions of Hayman's equation

Abstract

We present a complete description of the form of transcendental meromorphic solutions of the second order differential equation equation† w''w-w'²+a w'w+b w²=αw+βw'+γ, equation where $a$, $b$, $α$, $β$ and $γ$ are all rational functions. Together with the Wiman--Valiron theory, we then show that any transcendental meromorphic solution $w$