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solutions des séries y^{\prime \prime}-y=0,y(0)=2,y(1)=e+1/e

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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 expand factor rationalize

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développer (2+x)⁵

Solution

32+80x+80x²+40x³+10x⁴+x⁵

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(2+x)⁵

Appliquer le théorème du binôme: (a+b)ⁿ=∑_i=0ⁿ(ni)a⁽ⁿ⁻ⁱ⁾bⁱ

a=2, b=x

=∑_i=0⁵(5i)2⁽⁵⁻ⁱ⁾xⁱ

Développer la somme

=5!0!(5−0)! · 2⁵x⁰+5!1!(5−1)! · 2⁴x¹+5!2!(5−2)! · 2³x²+5!3!(5−3)! · 2²x³+5!4!(5−4)! · 2¹x⁴+5!5!(5−5)! · 2⁰x⁵

Simplifier 5!0!(5−0)! · 2⁵x⁰: 32

Simplifier 5!1!(5−1)! · 2⁴x¹: 80x

Simplifier 5!2!(5−2)! · 2³x²: 80x²

Simplifier 5!3!(5−3)! · 2²x³: 40x³

Simplifier 5!4!(5−4)! · 2¹x⁴: 10x⁴

Simplifier 5!5!(5−5)! · 2⁰x⁵: x⁵

=32+80x+80x²+40x³+10x⁴+x⁵

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

solutions des séries y^{\prime \prime}-y=0,y(0)=2,y(1)=e+1/e

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