Abstract
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.