The input can be written as:
As given, the LTI system is initially at rest. Hence, since for , thus, for (By the definition of causality).
Now we recursively insert values of input in the difference equation.
Putting:
, Thus, .
, y [-1] + 2y [-2] = x [-1] + 2x [-3 ] Thus, .
, . Thus, .
and so on.
Thus the output y[n] becomes as shown
Thus we see that the output is unbounded.
for 
, thus, 
for 
(By the definition of causality). 
in the difference equation. 
, 
Thus, 
. 
, y
[-1] + 2y [-2] = x [-1] + 2x [-3 ] Thus, 
. 
, 
. Thus, 
. 
, 
. Thus, 
. 
, 
. Thus, 
. 
, 
. Thus, 
. 
, 
. Thus, 
. 
, 
. Thus, 
. 
, 
. Thus, 
. 
