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Given a first-order autonomous algebraic ordinary differential equation, wepresent a method for computing formal power series solutions by means ofplaces. We provide an algorithm for computing a full characterization ofpossible initial values, classified in terms of the number of distinct formalpower series solutions extending them. In addition, if a particular initialvalue is given, we present a second algorithm that computes all the formalpower series solutions, up to a suitable degree, corresponding to it.Furthermore, when the ground field is the field of the complex numbers, weprove that the computed formal power series solutions are all convergent insuitable neighborhoods.

Solving First Order Autonomous Algebraic Ordinary Differential Equations by Places