z transform question.

[angel23]

1. The problem statement, all variables and given/known data
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)





3. The attempt at a solution
let A=0.3679 and B=0.3642
i took z transform for both sides so it became.
z^2 x(z)-z^2x(0)-zx(1)-A[zx(z)-zx(0)]+Ax(z)=A[zu(z)-zu(0)]+Bu(z)
x(z)[z^2-Az+A]+x(0)[Az-z^2]-zx(1)=A[zu(z)-zu(0)]+Bu(z)
x(z)[z^2-Az+A]=A[zu(z)-zu(0)]+Bu(z)-x(0)[Az-z^2]+zx(1)

then what can i do?
also how can i make use of u(1)=0.2142
u(2)=-0.2142
i am too confused and need help.

[Manchot]

To solve the problem, you need to specify some initial conditions. As it stands, it's unsolvable.

[angel23]

this is the full question given to me to solve and i am sure it is complete.

[xhatemx]

late reply ,, have you known the correct solution ?

the key that the input is not a step function , u have to use the u(0) , u(1) ... etc to draw the input and find expression to it .