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.