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Use the Laplace transform to solve the following initial value problem: x?=12x+3y y?=?9x+e^(3t) x(0)=0, y(0)=0 Let X(s)=L{x(t)}, and Y(s)=L{y(t)}. Find the...

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Advance Math

Use the Laplace transform to solve the following initial valueproblem:

x?=12x+3y

y?=?9x+e^(3t)

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 ofboth differential equations and solving for Y(s) and X(s):

X(s)=

Y(s)=

Find the partial fraction decomposition of X(s)X(s) and Y(s)Y(s)and their inverse Laplace transforms to find the solution of thesystem of DEs:

x(t)

y(t)

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