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 xn+1=axn+bxn2cxn+dxn−1,n=0,1,…, where the initial conditions x−1,x0x−1,x0 are arbitrary positive real numbers and a,b,c,da,b,c,d are positive constants. Also, we obtain the form of the solution of some special cases of this equation.