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
