series solution 16y^{\prime \prime}-8y^{\prime}+y=0,y(0)=40

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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

simplify solve for inverse tangent line

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Steps Examples

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laplace transform e^xx

Solution

1(s−1)²

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Solution steps

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L{e^xx}

Use Laplace Transform table: L{t^kf(t)}=(−1)^kd^kds^k (L{f(t)})

For e^xx: f(x)=e^x, k=1

=(−1)¹dds (L{e^x})

L{e^x}: 1s−1

dds (1s−1 )=−1(s−1)²

=(−1)¹(−1(s−1)² )

=1(s−1)²

Solve instead

inverse laplace e^xx

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Notebook

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

series solution 16y^{\prime \prime}-8y^{\prime}+y=0,y(0)=40

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