inverse of laplace (3x+9)/(2-x)

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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inverse laplace 3x+92−x

Solution

−3δ(t)−15e^2t

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Solution steps

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L⁻¹{3x+92−x }

Take the partial fraction of 3x+92−x : −3+15−x+2

=L⁻¹{−3+15−x+2 }

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{3}+L⁻¹{15−x+2 }

L⁻¹{3}: 3δ(t)

L⁻¹{15−x+2 }: −15e^2t

=−3δ(t)−15e^2t

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