Abstract
We look for solutions of the functional-differential equation \(f(\varphi (z))=a(z)f(z)f^\prime (z)\) for given series \(\varphi \) and \(a\). We show that all formal solutions \(f\) of this equation are local analytic. In order to do this we transform the equation to a special type of Briot–Bouquet differential equation.
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