Solution 3.8.1.14 Applying the Laplace transform, assuming zero initial conditions, yields s 4 Y (s)+12s 3 Y (s)+52s 2 Y (s)+96sY (s)+64Y (s)=U(s)+2sU(s)+s 2 U(s);; or (s 4 +12s 3 +52s 2 +96s +64)Y (s)=U(s)(s 2 +2s +1): Rearranging yields Y (s) U(s) = s 2 +2s +1 s 4 +12s 3 +52s 2 +96s +64 : 1