The Laplace transform of the function {left({2}{t}-{3}right)}{e}^{{frac{{{t}+{2}}}{{3}}}} is equal to: a) {e}^{{frac{2}{{3}}}}{left(frac{2}{{left({s}-

Alyce Wilkinson 2021-01-15 Answered
The Laplace transform of the function (2t3)et+23 is equal to:
a) e23(2(s13)23s13)
b) e23(2(s13)23s13)
c) e23(6(s13)2)
d) (2(s13)2+23)
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Expert Answer

hosentak
Answered 2021-01-16 Author has 100 answers
Step 1
Given that
(2t3)et+23
To find the Laplace transformation of given function
Step 2
Given
(2t3)et+23
=2tet+233et+23
Apply Laplace transform on both side
L{(2t3)et+23}=L{2tet+233et+23}
=L{2tet+23}L{3et+23}
=2L{tet3e23}L{3et3e23}
=2e23L{tet3}3e23L{et3}
=2e231(s13)23e231s13
[because  L{teat}=1(sa)2L{eat}=1sa]
=e23[2(s13)23s13]
L{(2t3)et+23}=e23[2(s13)23s13]
Answer A
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