New Solvable System OF 2 First-Order Nonlinearly-Coupled Ordinary Differential Equations

TL;DR

This paper introduces a simple, explicitly solvable autonomous system of two nonlinearly-coupled first-order ODEs with a specific algebraic structure, along with an isochronous variant with four variables.

Contribution

It presents a new class of solvable nonlinear ODE systems with explicit solutions and explores an isochronous extension with additional variables and parameters.

Findings

Explicit algebraic solutions for the introduced ODE system

Identification of an isochronous variant with specific properties

The model's simplicity and parameterization facilitate analysis and potential applications

Abstract

In this short communication we introduce a rather simple autonomous system of 2 nonlinearly-coupled first-order Ordinary Differential Equations (ODEs), whose initial-values problem is explicitly solvable by algebraic operations. Its ODEs feature 2 right-hand sides which are the ratios of 2 homogeneous polynomials of first degree divided by the same homogeneous polynomial of second degree. The model features only 4 arbitrary parameters. We also report its isochronous variant featuring 4 nonlinearly-coupled first-order ODEs in 4 dependent variables, featuring 9 arbitrary parameters.