On a functional-differential equation of A. F. Beardon and functional-differential equations of Briot-Bouquet type (Q380802)

This paper is concerned with the functional differential equation \[ f(\phi(z))=\alpha (z)f(z)f'(z), \] where \(\phi\) and \(\alpha\) are given local analytic functions. Then, by transforming the above equation to a special type of the Briot-Bouquet differential equation, the authors prove that all formal solutions \(f\) with \(f(0)=0\) and not zero everywhere, are local analytic.