- #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?

- 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

- 2,591

- 5

- #3

- 565

- 2

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

- 2,591

- 5

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

- #5

- 565

- 2

this is what the table has.

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

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

Last edited by a moderator:

- #6

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 961

Of course, you

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

using integration by parts.

- #7

- 565

- 2

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

- #8

- 124

- 0

[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

Science Advisor

Homework Helper

- 41,833

- 961

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

- 565

- 2

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?

Last edited by a moderator:

- #11

- 124

- 0

- #12

- 565

- 2

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

- Last Post

- Replies
- 5

- Views
- 903

- Last Post

- Replies
- 3

- Views
- 12K

- Last Post

- Replies
- 7

- Views
- 980

- Last Post

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 5

- Views
- 1K

- Last Post

- Replies
- 4

- Views
- 3K

- Last Post

- Replies
- 11

- Views
- 899

- Last Post

- Replies
- 41

- Views
- 2K

- Last Post

- Replies
- 6

- Views
- 3K

- Last Post

- Replies
- 3

- Views
- 665