Solution 3.8.1.13
Applying the Laplace transform, assuming zero initial conditions, yields
s
4
Y (s)+15s
3
Y (s)+74s
2
Y (s)+135sY (s)+72Y (s)=U(s)+sU(s);;
or
(s
4
+15s
3
+74s
2
+135s +72)Y (s)=U(s)(s +1):
Rearranging yields
Y (s)
U(s)
=
s +1
s
4
+15s
3
+74s
2
+135s +72
:
1