z transform question?

Question

consider the difference equation
x(n+2)-0.3679x(n+1)+0.3679x(n)=0.3679u(n+1)+u(n)
where u(n) is the input and given by
u(n)=0 n<0
u(0)=1
u(1)=0.2142
u(2)=-0.2142
u(n)=0 n=3,4,5.......
determine the output x(n)

x(n+2)-0.3679x(n+1)+0.3679x(n)=0.3679u(n+1)+u(n)

x(n+2)-0.3679x(n+1)
+0.3679x(n)=0.3679u(n+1)+u(n)

Answer 1

So u[n] = d[n] + 0.2142d[n-1] - 0.2142d[n-2], where d[n] is the delta function.

Since I can see the whole equation it's going to be hard for me to say more.

Take the z-transfrom and you'll get something like
X(z){z^2 - 0.3679z + 0.3679 + ...} = {1+0.2142z^-1 - 0.2142z^-2}

Divide to get X(z) = { top } / { bot }
take the inverse z-transform (you will probably have to do partial fraction expansion)

Answer 2

evaluate applying partial growth z/( z-a million)^3 = a million/(z-a million)^2 + a million /(z-a million)^3 then confer with z remodel pairs. i don't have the reference pair handy however the result's f(n) = a million/2 n^2 -- (a million/2)n