The difference equation r epresentat ion for a system is

The difference equation r epresentat ion for a system is
y[n] – 1/2 y[n – 1] = 2x[n], y[– 1] = 3
The natural response of system is

Characteristic equation is,

r -	1	= 0
	2

∴ y⁽ⁿ⁾ = C		1		ⁿ
		2

y[- 1] = 3 = C		1		^-1	, C =	3
		2				2

y⁽ⁿ⁾[n] =	3		1		^-1	u[n]
	2		2