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series solution y^{\prime \prime}+6y=0

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

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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 y^{′ ′}+6y=0

Solution

y=c₁(1−3t²+3t⁴2 +… +(−1)ⁿ· 36t²ⁿ· 3(1)(2)(3)(4)… n(2n−1) +… )+c₂(t−t³+3t⁵10 +… +(−1)ⁿ· 36t²ⁿ⁺¹· 3(2)(3)(4)(5)… n(2n+1) +… )

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y′ ′ +6y=0

Solve using series method: y=c₁(1−3t²+3t⁴2 +… +(−1)ⁿ· 36t²ⁿ· 3(1)(2)(3)(4)… n(2n−1) +… )+c₂(t−t³+3t⁵10 +… +(−1)ⁿ· 36t²ⁿ⁺¹· 3(2)(3)(4)(5)… n(2n+1) +… )