Abstract. We give a new proof of the fact that any meromorphic solution of a second order Briot--Bouquet differential equation in the whole plane is a degenerate or non-degenerate elliptic function. Our argument does not depend on the first order case.

AMS Subject Classification (1991): 34A20, 30D05

Keyword(s): Briot--Bouquet differential equations

Received April 28, 2009, and in revised form August 17, 2010. (Registered under 59/2009.)