- #1

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but looking it at the table, it looks like there's two different possible solutions for it.

one is for t^(n) x f(t)

and the other is for e^(at) x f(t)

which one do i choose?

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- Thread starter Ry122
- Start date

- #1

- 565

- 2

but looking it at the table, it looks like there's two different possible solutions for it.

one is for t^(n) x f(t)

and the other is for e^(at) x f(t)

which one do i choose?

- #2

Defennder

Homework Helper

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- #3

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i do get two different answers.

doesnt ur table have t^(n) x f(t)? wouldnt that also satisfy it?

doesnt ur table have t^(n) x f(t)? wouldnt that also satisfy it?

- #4

Defennder

Homework Helper

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My table doesn't have that one. What are your answers for each?

- #5

- 565

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this is what the table has.

http://users.on.net/~rohanlal/2222.jpg [Broken]

http://users.on.net/~rohanlal/2222.jpg [Broken]

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- #6

HallsofIvy

Science Advisor

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Of course, you

[tex]L(s)= \int_0^\infty t e^{3t}e^{-st}dt[/tex]

using integration by parts.

- #7

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so if i used the one in my previous post, that would that be incorrect?

- #8

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[tex]\displaystyle \mathcal{L}[e^{at}f(t)] = F(s-a),[/tex]

where [tex]F(s) = \mathcal{L}[f(t)].[/tex] Using this, you only need to get the Laplace transform of [tex]t[/tex], and evaluate it at [tex]s-3[/tex]. You should get the same result with both properties.

Good luck.

- #9

HallsofIvy

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a)[tex]\displaystyle \mathcal{L}[e^{at}f(t)] = F(s-a),[/tex]

where F(s) is the Laplace transform of t.

b)[tex]\displaystyle \mathcal{L}[tf(t)]= -F'(s)[/tex]

where F(s) is the Laplace transform of [itex]e^{3t}[/itex].

c)[tex]\displaystyle \mathcal{L}[te^{at}]= \int_0^\infty te^{(-s+3)t}dt[/tex]

will give the

It would be a good exercise to try each method and see.

- #10

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for the laplace transform of t^2 x e^(3t) (n is greater than 1)

would http://users.on.net/~rohanlal/2222.jpg [Broken] be the correct one to use?

would http://users.on.net/~rohanlal/2222.jpg [Broken] be the correct one to use?

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- #11

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- #12

- 565

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can you reread my previous post, i put in the wrong url for the image.

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