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laplace transform y^{\prime \prime}+6y^{\prime}+13y=0,y(0)=0

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

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ddx ((20x³−8x²+12x−7)+(−10x³+11x²−14x+6))

Solution

30x²+6x−2

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Solution steps

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ddx ((20x³−8x²+12x−7)+(−10x³+11x²−14x+6))

Apply the Sum/Difference Rule: (f±g)′=f ′±g′

=ddx (20x³)−ddx (8x²)+ddx (12x)−ddx (7)−ddx (10x³)+ddx (11x²)−ddx (14x)+ddx (6)

ddx (20x³)=60x²

ddx (8x²)=16x

ddx (12x)=12

ddx (7)=0

ddx (10x³)=30x²

ddx (11x²)=22x

ddx (14x)=14

ddx (6)=0

=60x²−16x+12−0−30x²+22x−14+0

Simplify

=30x²+6x−2

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

laplace transform y^{\prime \prime}+6y^{\prime}+13y=0,y(0)=0

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