Exact solutions to homogeneous and quasi-homogeneous systems of nonlinear ODEs

TL;DR

This paper provides exact solutions for broad classes of homogeneous and quasi-homogeneous nonlinear ODE systems, using elementary functions, enhancing analytical methods for solving complex differential equations.

Contribution

It introduces explicit solutions for general quasi-homogeneous and homogeneous nonlinear ODE systems involving arbitrary functions, expanding the set of solvable cases.

Findings

Exact solutions expressed in elementary functions for quasi-homogeneous systems.

Solutions applicable to systems with arbitrary functions of several arguments.

Enhanced understanding of the structure of nonlinear ODE solutions.

Abstract

This note considers fairly general quasi-homogeneous systems of first-order nonlinear ODEs and homogeneous systems of second-order nonlinear ODEs that contain arbitrary functions of several arguments. It presents several exact solutions to these systems in terms of elementary functions.