Abstract
In this paper we give an elementary proof of the famous theorem of J. Malmquist from 1913 and its refinement given by N. Steinmetz 1978. This result says, that if a differential equation of type (1.1) has a transcendental meromorphic solution, then it can be transformed into one of the six normalforms given in theorem 3.2 or a power of it. In this note we make no use of Nevanlinna's theory or the theory of central index used in former proofs. We only need the theorem of Liouville and the wellknown inequalities for meromorphic functions g with a finite number of poles, the Euclidean algorithm and a lemma of E Borel about monotone continuous functions.
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