Question: Solve the initial value problem below using the method of Laplace transforms.y double prime plus y prime minus 12 y equals negative 4 cosine t

Solve the initial value problem below using the method of Laplace transforms.y double prime plus y prime minus 12 y equals negative 4 cosine t minus 8 sine ty+y12y=4cost8sint,y left parenthesis StartFraction pi Over 2 EndFraction right parenthesis equals 1y2=1,y prime left parenthesis StartFraction pi Over 2 EndFraction right parenthesis equals 0

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