Page 66 - LAPLACE TRANSFORM

A
X(s) = 8 + 2s = + B
s (s−4) s (s−4)
−
= +
( −4)
4t
x(t) = − + 4e

Example 2

By using Laplace transform, find the time domain y(t) for the given function.

dy -2t
2 + 6y = 10e ; given y (0) =0
dt

Solution

dy -2t
2 + 6y = 10e
dt
2y’ + 6y = 10
(s+2)

2{sY(S) – y (0)} + 6Y(S) = 10
(s+2)

2{sY(S) – 0} + 6Y(S) = 10
(s+2)

2{sY(S)} + 6Y(S) = 10
(s+2)

Y(S) [2s + 6] = 10
(s+2)

Y(S) = 10
(s+2)(2s+6)

Y(S) = 10
(s+2).2(s+3)

Y(S) = 5 = A + B
(s+2)(s+3) (s+2) (s+3)

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