Given the difference equation y(k+ 2) / v(k + 1) + v(k) = e(k) where y(0) =

Given the difference equation

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y(k+ 2) / v(k + 1) + v(k) = e(k) where y(0) = y(1) = 0, e(0) = 0, and e(k) = 1, k = 1, 2,... . (a) Solve for y(k) as a function of k, and give the numerical values of y(k), 0k 4. (b) Solve the difference equation directly for y(k), 0k 4, to verify the results of part (a). (c) Repeat parts (a) and (b) for e(k) = 0 for all k, and y(0) = 1, y(1) = -2.