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inverse of laplace (x^2-25)/(x^2+4x-5)

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

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inverse laplace x²−25x²+4x−5

Solution

δ(t)−4e^t

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L⁻¹{x²−25x²+4x−5 }

Take the partial fraction of x²−25x²+4x−5 : 1−4x−1

=L⁻¹{1−4x−1 }

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{1}−L⁻¹{4x−1 }

L⁻¹{1}: δ(t)

L⁻¹{4x−1 }: 4e^t

=δ(t)−4e^t

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

inverse of laplace (x^2-25)/(x^2+4x-5)

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