series solution y^{\prime\prime}-xy=0

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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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series solution y^{′ ′}−xy=0

Solution

y=c₁(1+x³6 +x⁶180 +… +x³ⁿ(2)(3)(5)(6)…(3n−1)· 3n +… )+c₂(x+x⁴12 +x⁷504 +… +x³ⁿ⁺¹(3)(4)(6)(7)… 3n(3n+1) +… )

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y′ ′ −xy=0

Solve using series method: y=c₁(1+x³6 +x⁶180 +… +x³ⁿ(2)(3)(5)(6)… (3n−1)· 3n +… )+c₂(x+x⁴12 +x⁷504 +… +x³ⁿ⁺¹(3)(4)(6)(7)… 3n(3n+1) +… )

y=c₁(1+x³6 +x⁶180 +… +x³ⁿ(2)(3)(5)(6)… (3n−1)· 3n +… )+c₂(x+x⁴12 +x⁷504 +… +x³ⁿ⁺¹(3)(4)(6)(7)… 3n(3n+1) +… )

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

series solution y^{\prime\prime}-xy=0

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