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frobenius method 4x^2y''-4x^2y'+(1-2x)y=0

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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

laplace bernoulli substitution linear exact

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inverse sin²(x)

Solution

arcsin(√x), arcsin(−√x)

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Function Inverse definition

A function g is the inverse of function f if for y=f(x), x=g(y)

Solve for sin(x), y=sin²(x)

sin(x)=√y, sin(x)=−√y

sin(a)=b ⇒ a=arcsin(b)

arcsin(√y), arcsin(−√y)

Substitute y=x

arcsin(√x), arcsin(−√x)

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domain sin²(x)

range sin²(x)

periodicity sin²(x)

Method of Frobenius ODE Examples

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

frobenius method 4x^2y''-4x^2y'+(1-2x)y=0

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