On Formal Power Series Solutions of Algebraic Ordinary Differential Equations

03/26/2018

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by   Yi Zhang, et al.

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We propose a computational method to determine when a solution modulo a certain power of the independent variable of a given algebraic differential equation (AODE) can be extended to a formal power series solution. The existence and the uniqueness conditions for the initial value problems for AODEs at singular points are included. Moreover, when the existence is confirmed, we present the algebraic structure of the set of all formal power series solutions satisfying the initial value conditions.