代数常微分方程形式幂级数解的存在唯一性
On Existence and Uniqueness of Formal Power Series Solutions of Algebraic Ordinary Differential Equations
摘要：
给出了一个代数常微分方程（AODE），提出了一种计算方法来确定截断幂级数何时可以扩展为形式幂级数解。如果给定的AODE或初始值满足一定的正则性条件，我们计算所有的解决方案。此外，当确定存在性时，我们给出了所有形式幂级数解的代数结构。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
