Correct Answer : Option (C) : y(n) = y(n-1) + y(n+1)
Explanation : We know that for a dynamic system, the present output of the system should depend only on the past output and the future output.
For y (n) = y (n-1), we can observe that output depends only on the past but not on the future. Hence it is not a dynamic system.
For y (n) = x (n), we can observe that output depends on the present. Hence it is not a dynamic system.
For y (n) + y (n+1) + y (n+3) = 0, we can observe that output is a constant. Hence it is not a dynamic system.
For y (n) = y (n-1) + y (n+1), we can observe that output depends only on past and future outputs. Hence it is a dynamic system.
