Page 67 - LAPLACE TRANSFORM

multiply each side with (s + 2)(s + 3)

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

5 = A( + ) + B( + )

when s = −2 5 = A( + ) + B( + )

5 = A(−2 + 3)

5 = A

when s = −3 5 = A( + ) + B( + )

5 = B(−3 + 2)

5 = −B

B = −

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

Y(S) = + −
(s+2) (s+3)

-2t
-3t
y(t) = 5e − 5e

Example 3

Determine the time domain x(t) for the given function by using Laplace transform.

5 ′ – 20x = 30e 3t ; given x (0) =2

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