laplace transform y^{\prime \prime}-10y^{\prime}+9y=5t,y(0)=-1,y^{\prime}(0)=2

Full pad

`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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prove sin³(x)+cos³(x)sin(x)+cos(x) =1−sin(x)cos(x)

Solution

True

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Solution steps

One step at a time

sin³(x)+cos³(x)sin(x)+cos(x) =1−sin(x)cos(x)

Manipulating left side

sin³(x)+cos³(x)sin(x)+cos(x)

Simplify cos³(x)+sin³(x)cos(x)+sin(x) : cos²(x)−sin(x)cos(x)+sin²(x)

=cos²(x)+sin²(x)−cos(x)sin(x)

Manipulating right side

1−sin(x)cos(x)

Rewrite using trig identities

=cos²(x)+sin²(x)−sin(x)cos(x)

We showed that the two sides could take the same form

⇒ True

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

laplace transform y^{\prime \prime}-10y^{\prime}+9y=5t,y(0)=-1,y^{\prime}(0)=2

Solution

Solution steps

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