# Two LaPlace Transform problems

• May 24th 2011, 03:31 PM
Hossam
Two LaPlace Transform problems
can i have the complete solution for these problems ??

i don't know how to start solving !!

http://i55.tinypic.com/2lcmp3o.jpg
• May 24th 2011, 03:47 PM
TheEmptySet
Quote:

Originally Posted by Hossam
can i have the complete solution for these problems ??

i don't know how to start solving !!

http://i55.tinypic.com/2lcmp3o.jpg

For the first one you will need to combine three different theorems

$\displaystyle \mathcal{L}\{ f'(t)\}=sF(s)-f(0)$

$\displaystyle \mathcal{L}\{ t^nf(t)\}=(-1)^n\frac{d^n}{ds^n}F(s)$

$\displaystyle \mathcal{L}\{ e^{at}f(t)\}=F(s-a)$

See if you can combine them to get the answer.

for 2 use the convolution theorem

$\displaystyle \mathcal{L}\{ \int_{0}^{t}f(t-\tau)g(\tau)d\tau\}=F(s)G(s)$
• May 24th 2011, 04:14 PM
Hossam
for problem 2 , convolution theorem says f(t-u) .. and here it's e^(x-t) .. so i have to take the ( - ) common so it becomes e^-(t-x) ??? is this right ?
• May 24th 2011, 04:17 PM
TheEmptySet
Quote:

Originally Posted by Hossam
for problem 2 , convolution theorem says f(t-u) .. and here it's e^(x-t) .. so i have to take the ( - ) common so it becomes e^-(t-x) ??? is this right ?

Yes that is correct!
• May 24th 2011, 04:21 PM
Hossam
Quote:

Originally Posted by TheEmptySet
Yes that is correct!

Okay , Thanks much