laplace transform 16y^{\prime \prime}-8y^{\prime}+y=0,y(0)=40

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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 inverse tangent line

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inverse (

4	7	10	19
20	−1	5	7
6	1	25	4
4	8	2	5

)

Solution

(

−2288917	89117834	−1482	51517834
−82726751	−2248917	4723	396526751
−10926751	−1058917	32723	−9226751
6388917	448917	−6241	−5258917

)

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Solution steps

One step at a time

(

4	7	10	19
20	−1	5	7
6	1	25	4
4	8	2	5

)⁻¹

Inverse matrix

A matrix is invertible if and only if there is a sequence of elementary row (or column) operations taking it to the identity matrix.

Augment with a 4x4 identity matrix

[

4	7	10	19	∣	1	0	0	0
20	−1	5	7	∣	0	1	0	0
6	1	25	4	∣	0	0	1	0
4	8	2	5	∣	0	0	0	1

]

Reduce the matrix on the left to the identity matrix

[

1	0	0	0	∣	−2288917	89117834	−1482	51517834
0	1	0	0	∣	−82726751	−2248917	4723	396526751
0	0	1	0	∣	−10926751	−1058917	32723	−9226751
0	0	0	1	∣	6388917	448917	−6241	−5258917

]

The inverse matrix is on the right side of the augmented matrix

−2288917	89117834	−1482	51517834
−82726751	−2248917	4723	396526751
−10926751	−1058917	32723	−9226751
6388917	448917	−6241	−5258917

)

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4	7	10	19
20	−1	5	7
6	1	25	4
4	8	2	5

) or choose below

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

laplace transform 16y^{\prime \prime}-8y^{\prime}+y=0,y(0)=40

Solution

Solution steps

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