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Solve the following difference equation using Z-transforms.) y(k) + 3y(k 1) + 2y(k 2) = x(k 1) + 3x(k 2) Given x(k) = u(k) and y(-1) = 1, y(-2) = 2 b....

Solve the following difference equation using Z-transforms.
a.) y(k) + 3y(k −1) + 2y(k − 2) = x(k −1) + 3x(k − 2)
Given x(k) = u(k) and y(-1) = 1, y(-2) = 2

b.) y(k +1) − y(k) = k^2 ; y(0) = 1

c.) Consider the following difference equation
y(k) − 0.4y(k −1) = x(k)

Given x(k)=2sin(π/2*k )*u(k)
Use Z-transforms to find y(k). Assume y(-1) = 0. Also use Z-transforms to find the initial
and final values of y(k); check your answers from y(k).
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