A note on the computation of Puiseux series solutions of the Riccatti equation associated with a homogeneous linear ordinary differential equation

TL;DR

This paper discusses methods for computing Puiseux series solutions of Riccatti equations linked to homogeneous linear ODEs, extending previous work on the complexity of solving polynomial differential equations with Puiseux series.

Contribution

It provides a detailed approach for computing Puiseux series solutions of Riccatti equations associated with linear ODEs, building on prior complexity analysis.

Findings

Detailed methodology for Puiseux series computation

Extension of previous complexity results

Improved understanding of Riccatti equation solutions

Abstract

We present in this paper a detailed note on the computation of Puiseux series solutions of the Riccatti equation associated with a homogeneous linear ordinary differential equation. This paper is a continuation of [1] which was on the complexity of solving arbitrary ordinary polynomial differential equations in terms of Puiseux series.