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derivative of x^3e^{-x^2}

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

☐²

x^☐

√☐

^□√☐

□□

log_□

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∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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series solution xy^{′ ′}+y^′+2xy=0

Solution

y=c₁(1−x²2 +x⁴16 +… +(−1)ⁿx²ⁿ16… 2n² +… )+c₂(ln(x)(1−x²2 +x⁴16 +… +(−1)ⁿx²ⁿ16… 2n² +… )+x²2 −3x⁴32 +11x⁶1728 +… )

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xy′ ′ +y′ +2xy=0

Solve using series method: y=c₁(1−x²2 +x⁴16 +… +(−1)ⁿx²ⁿ16… 2n² +… )+c₂(ln(x)(1−x²2 +x⁴16 +… +(−1)ⁿx²ⁿ16… 2n² +… )+x²2 −3x⁴32 +11x⁶1728 +… )

y=c₁(1−x²2 +x⁴16 +… +(−1)ⁿx²ⁿ16… 2n² +… )+c₂(ln(x)(1−x²2 +x⁴16 +… +(−1)ⁿx²ⁿ16… 2n² +… )+x²2 −3x⁴32 +11x⁶1728 +… )

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

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derivative of x^3e^{-x^2}

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