Given the difference equation where x(k+ 2) + 5x(k + 1) + 4x(k) = e(k) 1, 0, e(k)= x(0) = 0 x(1) = -1 k = 0 otherwise (a) Solve for x(k) as a function of k. (b) Evaluate x(0), x(1), x(2), and x(3) in part (a). (c) Verify the results in part (b) using the power-series method. (d) Verify the results in part (b) by solving the difference equation directly.

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Given the difference equation
where
x(k+ 2) + 5x(k + 1) + 4x(k) = e(k)
k=0
[1,
e(k)= 10, otherwise
x(0) = 0
x(1) = -1
(a) Solve for x(k) as a function of k.
(b) Evaluate x(0), x(1), x(2), and x(3) in part (a).
(c) Verify the results in part (b) using the power-series method.
(d) Verify the results in part (b) by solving the difference equation directly.
Transcribed Image Text:Given the difference equation where x(k+ 2) + 5x(k + 1) + 4x(k) = e(k) k=0 [1, e(k)= 10, otherwise x(0) = 0 x(1) = -1 (a) Solve for x(k) as a function of k. (b) Evaluate x(0), x(1), x(2), and x(3) in part (a). (c) Verify the results in part (b) using the power-series method. (d) Verify the results in part (b) by solving the difference equation directly.
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