Onsider the difference equation- where xk is the output and

Question

Consider the difference equation

x(k + 2) - 1.3679x(k + 1) + 0.3679x(k) = 0.3679u(k + 1) + 0.2642u(k)

where x(k) is the output and x(k) = 0 for k<=0 and where u(k) is the input and is given by

u(k) = 0,        k <0

u(0) = 1

u(1) = 0.2142

u(2) = -0.2142

u(k) = 0,         k = 3,4,5

Determine the output x(k).