Qualitative behavior of difference equation of order two

In this paper we deal with the qualitative behavior of the solutions of the following difference equation x n + 1 = a x n + b x n 2 c x n + d x n − 1 , n = 0 , 1 , … , where the initial conditions x − 1 , x 0 are arbitrary positive real numbers and a , b , c , d are positive constants. Also, we obtain the form of the solution of some special cases of this equation.