Use the Laplace transform to solve the following initial value problem: x' = 13x +5y, y = -8x + est x(0)= 0, y(0) = 0 Let X(s) L{x(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: x(t) = y(t)

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A: We will find out the required solution.

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A: Given that, the differential equation need to solve it using the Laplace transformation.

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