Explicit Expression for a First Integral for a Class of Two-dimensional Differential System

Volume 6, Issue 1, Article 2 - 2019

Authors: Rachid Boukoucha;Mouna Yahiaoui

Copyright © 2019 . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abstract

In this paper we are intersted in studying the existence of a first integral and to the curves which are formed by the trajectories of the two-dimensional differential systems of the form    x′ = P (x,y) + x(λxexp(M(x,y) N(x,y))+ βy exp(R(x,y) S(x,y))),y ′ = Q(x,y) + y(λxexp(M(x,y) N(x,y))+ βy exp(R(x,y) S(x,y))), where P (x,y), Q(x,y), M (x,y), N (x,y), R(x,y), S (x,y) are homogeneous polynomials of degree a, a, b, b, c, c respectively and λ, β ∈R. Concrete examples exhibiting the applicability of our result are introduced.

How To Cite This Article

Rachid Boukoucha;Mouna Yahiaoui (2019) Explicit Expression for a First Integral for a Class of Two-dimensional Differential System
General Letters in Mathematics Vol 6 (1) 10-15