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laplace transform 2cos^3(x)

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laplace transform 2cos³(x)

Solution

s2(s²+9) +3s2(s²+1)

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Solution steps

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L{2cos³(x)}

Rewrite using trig identities

L{12 cos(3x)+32 cos(x)}

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

=12 L{cos(3x)}+32 L{cos(x)}

L{cos(3x)}: ss²+9

L{cos(x)}: ss²+1

=12 · ss²+9 +32 · ss²+1

Refine 12 · ss²+9 +32 · ss²+1 : s2(s²+9) +3s2(s²+1)

=s2(s²+9) +3s2(s²+1)

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inverse laplace 2cos³(x)

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

laplace transform 2cos^3(x)

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