Question: Take the Laplace transform of the following initial value problem and solve for Y(s)=L{y(t)} :y''-6y'-27y={1,0t <1y(0)=0y'(0)=00,1tY(s)=1-e-ss(s-9)(s+3).Now find the inverse transform:y(t)=-127+136e-3t+1108e9t-u(t-1)(-127+136e-3t(t-1)+1108e9(t-1))u(t-c) for the Heaviside step function

Take the Laplace transform of the following initial value problem and solve for Y(s)=L{y(t)} :y''-6y'-27y={1,0t<1y(0)=0y'(0)=00,1tY(s)=1-e-ss(s-9)(s+3).Now find the inverse transform:y(t)=-127+136e-3t+1108e9t-u(t-1)(-127+136e-3t(t-1)+1108e9(t-1))u(t-c) for the Heaviside step function uc(t) with step att=c.1s(s-9)(s+3)=-127s+136s+3+1108s-9

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