Solving Z Transform of Difference Equation: x(n+2)-0.3679x(n+1)+0.3679x(n)

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The discussion revolves around solving the difference equation x(n+2) - 0.3679x(n+1) + 0.3679x(n) = 0.3679u(n+1) + u(n), where u(n) is defined for specific values. Participants emphasize the necessity of specifying initial conditions to solve the equation, noting that without them, the problem remains unsolvable. The input function u(n) is not a simple step function, requiring careful consideration of its defined values at u(0), u(1), and u(2) to derive the correct output x(n). Clarification on how to utilize these values in the Z-transform process is sought, indicating a need for further guidance. The conversation highlights the complexities involved in applying the Z-transform to difference equations with non-standard inputs.
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Homework Statement


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)





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.
 
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To solve the problem, you need to specify some initial conditions. As it stands, it's unsolvable.
 
this is the full question given to me to solve and i am sure it is complete.
 
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 .
 
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