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