Question: Use the Laplace transform to solve the following initial value problem:y''+8y'+16y=0,y(0)=-6,y'(0)=-4First, using Y for the Laplace transform ofy(t),i.e.,Y=L{y(t)},find the equation you get by taking the

Use the Laplace transform to solve the following initial value problem:y''+8y'+16y=0,y(0)=-6,y'(0)=-4First, using Y for the Laplace transform ofy(t),i.e.,Y=L{y(t)},find the equation you get by taking the Laplace transform of the differential equation=0Now solve for Y(s)=-6s-52(s+4)2and write the above answer in its partial fraction decomposition, Y(s)=As+a+B(s+a)2Y(s)=+Now by inverting the transform, find y(t)=

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