Use the Laplace transform to solve the following initial value problem: x' = 9x + 4y, y = -5x + et 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: (1)let a and b constants , then L(af(t)+bg(t))=aL(f(t))+bL(g(t)).(2) L(eat)=1s−a

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Q: Use the Laplace transform to solve the following initial value problem: x' = 13x +5y, y = -8x + est…

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