  Given an autonomous first order algebraic ordinary differential equation
F(y,y')=0, we prove that every formal Puiseux series solution, expanded around
any finite point or at infinity, is convergent. The proof is constructive and
we provide an algorithm to describe all such Puiseux series solutions.
Moreover, we show that for any point in the complex plane there exists a
solution of the differential equation which defines an analytic curve passing
through this point.
