Question: Use the Laplace transform to solve the following initial value problem: =12z +4y, y =8z +e z(0) =0, y(0) =0 Let X(s) = {z(t)}, and

Use the Laplace transform to solve the following initial value problem: =12z +4y, y =8z +e z(0) =0, y(0) =0 Let X(s) = {z(t)}, and Y(s) = L{y(t)}. Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y (s) and X(s): X(s) = Y(s) = Find the partial fraction decomposition of X(s) and Y(s) and their inverse Laplace transforms to find the solution of the system of DEs: y(t) =

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