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series solution 4y^{\prime \prime}-6y^{\prime}+7y=0

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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

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Generated by AI

e^{(1 0 0
0 1 0
0 0 1
)}

Solution

(

`e`	0	0
0	`e`	0
0	0	`e`

)

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Solution steps

One step at a time

e^{(1 0 0
0 1 0
0 0 1
)}

For diagonal matrix A=(

`a`₁₁	0	⋯	0
0	`a`₂₂	⋯	0
⋮	⋮	⋱	⋮
0	0	⋯	`a`_nn

) the matrix exponential is
e^A=(

`e`^a₁₁	0	⋯	0
0	`e`^a₂₂	⋯	0
⋮	⋮	⋱	⋮
0	0	⋯	`e`^a_nn

)

`e`¹	0	0
0	`e`¹	0
0	0	`e`¹

)

Simplify each element

`e`	0	0
0	`e`	0
0	0	`e`

)

Homogenous Ordinary Differential Equations (ODE) Examples

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أهلاً, اطرح سؤالا حول e^{(1 0 0
0 1 0
0 0 1
)} أو اختر أدناه

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

series solution 4y^{\prime \prime}-6y^{\prime}+7y=0

Solution

Solution steps

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