# Thread: Two LaPlace Transform problems

1. ## Two LaPlace Transform problems

can i have the complete solution for these problems ??

i don't know how to start solving !!

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

i don't know how to start solving !!

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

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

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

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

See if you can combine them to get the answer.

for 2 use the convolution theorem

$\mathcal{L}\{ \int_{0}^{t}f(t-\tau)g(\tau)d\tau\}=F(s)G(s)$

3. 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 ?

4. 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!

5. Originally Posted by TheEmptySet
Yes that is correct!
Okay , Thanks much