From the introduction: R. P. Agarwal and E. M. Elsayed [Adv. Stud. Contemp. Math., Kyungshang 17, No. 2, 181–201 (2008; Zbl 1169.39001)] studied solutions of some particular cases of the following classes of the difference equations
where and . Explicit solutions of some subclasses of these equations are given. Our aim is to give short proofs of the main results of the above authors as well as to extend some of them.