uonenba x(k + 2) + 3x(k + 1) + 2r(k) = e(k) %3D where k = 0 otherwise 1, e(k) = %3D 0, x(0) = 1 %3! 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.
uonenba x(k + 2) + 3x(k + 1) + 2r(k) = e(k) %3D where k = 0 otherwise 1, e(k) = %3D 0, x(0) = 1 %3! 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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Transcribed Image Text:2-13. Given the difference equation
x(k + 2) +3x(k + 1) + 2r(k) = e(k)
%3D
where
k = 0
e(k) =
0,
otherwise
x(0) = 1
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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