Given an algebraic ordinary differential equation (AODE), we propose a computational method to determine when a truncated power series can be extended to a formal power series solution. If a certain regularity condition on the given AODE or on the initial values is fulfilled, we compute all of the solutions. Moreover, when the existence is confirmed, we present the algebraic structure of the set of all formal power series solutions.

翻译：考虑到代数普通差分方程( ASOD), 我们建议一种计算方法, 以确定何时可以将短耗的电量序列扩展为正式的电量序列解决方案。 如果满足了给定的AODE或初始值的某种规律性条件, 我们计算所有解决方案。 此外, 当确认存在时, 我们给出了所有正式电量序列解决方案组的代数结构 。