Armengol Gasull, Hector Giacomini
Published 2020-06-16Version 1
In this work we consider a given root of a family of n-degree polynomials as a one-variable function that depends only on the independent term. Then we prove that this function satisfies several ordinary differential equations (ODE). More concretely, it satisfies several simple separated variables ODE, a first order generalized Abel ODE of degree n-1 and an (n-1)-th order linear ODE. Although some of our results are not new, our approach is simple and self-contained. For n=2, 3 and 4 we recover, from these ODE, the classical formulas for solving these polynomials.
Connection coefficients and monodromy representations for a class of Okubo systems of ordinary differential equations, II
On periodic approximate solutions of ordinary differential equations
Oscillation, suboscillation and nonoscillation criteria for linear systems of ordinary differential equations
![QR code for arXiv:2006.09362 [math.CA]](http://oss.arxitics.com/images/favicon.svg)