Solution 2.9.5.8
Applying the Laplace transform yields
s
2
Y (s);sy(0);y
[1]
(0);4Y (s)=0:
Rearranging yields
(s
2
;4)Y (s)=sy(0) + y
[1]
(0);;
or
Y (s)=
sy(0) + y
[1]
(0)
(s;2)(s +2)
For the given initial conditions we then have
Y (s) =
s ;2
(s +2)(s;2)
=
1
s +2
:
y(t)=e
;2t
1(t)
1