  We prove that the binary complexity of solving ordinary polynomial
differential equations in terms of Puiseux series is single exponential in the
number of terms in the series. Such a bound was given by Grigoriev [10] for
Riccatti differential polynomials associated to ordinary linear differential
operators. In this paper, we get the same bound for arbitrary differential
polynomials. The algorithm is based on a differential version of the
Newton-Puiseux procedure for algebraic equations.
