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inverse of laplace (x-4)/(x^2-5x+6)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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inverse laplace x−4x²−5x+6

Solution

2e^2t−e^3t

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L⁻¹{x−4x²−5x+6 }

Take the partial fraction of x−4x²−5x+6 : 2x−2 −1x−3

=L⁻¹{2x−2 −1x−3 }

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−2 }−L⁻¹{1x−3 }

L⁻¹{2x−2 }: 2e^2t

L⁻¹{1x−3 }: e^3t

=2e^2t−e^3t

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

inverse of laplace (x-4)/(x^2-5x+6)

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