Solution 3.8.1.9
Applying the Laplace transform, assuming zero initial conditions, yields
s
3
Y (s)+10s
2
Y (s)+32sY (s)+32Y (s)=U(s);;
or
(s
3
+10s
2
+32s +32)Y (s)=U(s):
Rearranging yields
Y (s)
U(s)
=
1
s
3
+10s
2
+32s +32
:
1