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inverse of laplace (32)/(x^2-64)

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(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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inverse laplace 32x²−64

Solution

−2e^−8t+2e^8t

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L⁻¹{32x²−64 }

Take the partial fraction of 32x²−64 : −2x+8 +2x−8

=L⁻¹{−2x+8 +2x−8 }

Use the linearity property of Inverse Laplace Transform:
For functions f(s), g(s) and constants a, b: L⁻¹{a·f(s)+b·g(s)}=a·L⁻¹{f(s)}+b·L⁻¹{g(s)}

=−L⁻¹{2x+8 }+L⁻¹{2x−8 }

L⁻¹{2x+8 }: 2e^−8t

L⁻¹{2x−8 }: 2e^8t

=−2e^−8t+2e^8t

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

inverse of laplace (32)/(x^2-64)

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