Question: Solve the following simultaneous differential equations using the Laplace transform, assum- ing all initial conditions to be zero and the input x(t) = u(t):

Solve the following simultaneous differential equations using the Laplace transform, assum- ing all initial conditions to be zero and the input x(t) = u(t): (a) (D+3)y (t) - 2y2 (t) = x(t) -2y1 (1)+(2D+4)y2(t) = 0 (b) (D+2)y (t) - (D+1)y (t) = 0 Ca - (D+1)yi (t) + (2D+1)y2 (t) = x(t) Determine the transfer functions relating outputs y (t) and y2 (t) to the input x(t).

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