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

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

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diretriz y=25−x²

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y=1014

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Diretriz de uma parábola

Uma parábola é o espaço de pontos tal que a distância a um ponto (o foco) equivale à distancia a uma reta (a diretriz)

Equação geral da parábola

4p(y−k)=(x−h)² é a equação geral da parábola de eixo vertical, com vértice em (h, k),
e distância focal |p|

Reescrever y=25−x² com a forma da equação geral da parábola: 4(−14 )(y−25)=(x−0)²

(h, k)=(0, 25), p=−14

A parábola é simétrica ao redor do eixo y (ordenadas) e, portanto, a diretriz é uma reta paralela ao eixo x (abscissas), uma distância −p do centro (0, 25) no eixo y (ordenadas)

y=25−p

y=25−(−14 )

Simplificar

y=1014

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

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

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

Solution

Solution steps

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