Solution 3.8.1.4 Applying the Laplace transform, assuming zero initial conditions, yields s 3 Y (s)+5s 2 Y (s)+12sY (s)+8Y (s)=U(s)+2sU(s)+s 2 U(s);; or (s 3 +5s 2 +12s +8)Y (s)=U(s)(s 2 +2s +1): Rearranging yields Y (s) U(s) = s 2 +2s +1 s 3 +5s 2 +12s +8 : 1