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laplace transform 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

laplace bernoulli substitution linear exact

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taylor xln(x)

Solution

(x−1)+12 (x−1)²−16 (x−1)³+112 (x−1)⁴−120 (x−1)⁵+…

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Solution steps

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Taylor Series

Taylor series of function f(x) at a is defined as:
f(x)=f(a)+f^′(a)1! (x−a)+f^′′(a)2! (x−a)²+f^′′′(a)3! (x−a)³+…

Apply the Taylor Formula

=0+ddx (xln(x))(1)1! (x−1)+d²dx² (xln(x))(1)2! (x−1)²+d³dx³ (xln(x))(1)3! (x−1)³+…

Evaluate Derivatives

=0+11! (x−1)+12! (x−1)²+−13! (x−1)³+24! (x−1)⁴+−65! (x−1)⁵+…

بسّط

=(x−1)+12 (x−1)²−16 (x−1)³+112 (x−1)⁴−120 (x−1)⁵+…

Homogenous Ordinary Differential Equations (ODE) Examples

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Notebook

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

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

Solution

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