Consider the following initial value problem y(t) = [-3/2 1/2 1/2 -3/2] y(t) + [0...
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Consider the following initial value problem y(t) = [-3/2 1/2 1/2 -3/2] y(t) + [0 h(t - 1)], y(0) = [1 0], where y(t) = [y_1(t) y_2(t)], where h(middot) denotes the Heaviside step function. (a) Determine Y(s), the Laplace transform of y(t). (Perform this calculation "by hand".) (b) Determine y(t) by computing the inverse Laplace transform of the two components of Y(s). (You may use Mathematica in part b if you wish. Provide complete documentation.) (c) Use Mathematica to plot both components of your solution, i.e. y_1(t) and y_2(t), on the same graph over the time interval 0 lessthanorequalto t lessthanorequalto 10. (Plot[{y1[t], y2[t]},{t, 0, 10}])
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