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laplace transform (x-3)e^x

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laplace transform (x−3)e^x

Solution

1(s−1)² −3s−1

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Solution steps

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L{e^x(x−3)}

Apply transform rule: if L{f(t)}=F(s) then L{e^atf(t)}=F(s−a)

For (x−3)e^x: f(x)=(x−3), a=1

=L{(x−3)}(s−1)

L{(x−3)}: 1s² −3s

=1(s−1)² −3(s−1)

=1(s−1)² −3s−1

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inverse laplace (x−3)e^x

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

laplace transform (x-3)e^x

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