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laplace transform y^{\prime \prime}-6y^{\prime}+15y=2sin(3t),y(0)=-1,y^{\prime}(0)=-4

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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

laplace bernoulli substitution linear exact

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Steps Examples

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(

1√6	−1√2	1√3
1√6	1√2	1√3
−2√6	0	1√3

)(

7	0	0
0	1	0
0	0	1

)(

1√6	−1√2	1√3
1√6	1√2	1√3
−2√6	0	1√3

)^T

Solution

(

2	1	−2
1	2	−2
−2	−2	5

)

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Solution steps

One step at a time

(

3	−5−16	2.5	−13
−2	5+16	−2.5	13
0	0	0	0
0	0	0	0
0	0	0	0
0	0	0	0

)^T(

)^T

(

3	−5−16	2.5	−13
−2	5+16	−2.5	13
0	0	0	0
0	0	0	0
0	0	0	0
0	0	0	0

)^T=(

3	−2	0	0	0	0
−5−16	5+16	0	0	0	0
2.5	−2.5	0	0	0	0
−13	13	0	0	0	0

)

3	−2	0	0	0	0
−5−16	5+16	0	0	0	0
2.5	−2.5	0	0	0	0
−13	13	0	0	0	0

)(

)^T

(

)^T=(

)

3	−2	0	0	0	0
−5−16	5+16	0	0	0	0
2.5	−2.5	0	0	0	0
−13	13	0	0	0	0

)(

)

(

3	−2	0	0	0	0
−5−16	5+16	0	0	0	0
2.5	−2.5	0	0	0	0
−13	13	0	0	0	0

)(

)=(

−3

313

−5

)

−3

313

−5

)

IVP using Laplace ODE Examples

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Hi, ask a question about (

3	−5−16	2.5	−13
−2	5+16	−2.5	13
0	0	0	0
0	0	0	0
0	0	0	0
0	0	0	0

)^T· (

)^T

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

laplace transform y^{\prime \prime}-6y^{\prime}+15y=2sin(3t),y(0)=-1,y^{\prime}(0)=-4

Solution

Solution steps

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