Page 73 - LAPLACE TRANSFORM

2
2{s Y(s) – s (4) – 9} + 5{s Y(s) – 4} − 3Y(s) = 0
2
2s Y(s) – 8s – 18 + 5sY(s) – 20 − 3Y(s) = 0

2
2s Y(s) + 5sY(s) − 3Y(s) = 8s + 18 + 20
2
Y(s) (2s + 5s – 3) = 8s + 38
Y(s) {(2s − 1) (s+3)} = 8s + 38

Y(s) = 8s + 38 = A + B
(2s − 1) (s+3) (2s − 1) (s+3)

+ = A ( + ) + B ( − )

when (2s − 1) = 0

1
s= ; + = A ( + ) + B ( − )
2
1 1
8( ) + 38 = A ( + 3)
2 2
1 6
4 + 38 = A ( + )
2 2
7
42 = A
2
84 = 7A

=

when (S + 3) = 0

s=−3; + = A ( + ) + B ( − )

8(−3) + 38 = B ( 2(−3) − 1)

−24 + 38 = −7B

14 = −7B

= = −2
−

− −
Y(s) = + = 1 +
(2s − 1) (s+3) 2 ( s − ) (s+3)
2

-3t
y(t) = e 1/2t − 2 e

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