# Laplace transforms? Inverse?

• Mar 8th 2012, 01:34 AM
ramdrop
Laplace transforms? Inverse?
Hey:

In my tutorial question, I firstly had to prove that the Laplace transform of a differential equation was:

L(t) = n!(s-1)^n
---------
s^n+1

This I have proved, now I need to find the Laplace transform of t*L(t) and then have to deduce the value of:

Integral between 0 and inf of : e^-2t * t*L(t)

I'm really stuck, sorry I can't do the Laplex stuff, hope you can understand it.
• Mar 8th 2012, 10:46 AM
Issler
Re: Laplace transforms? Inverse?
this question doesn't make any sense
• Mar 8th 2012, 11:14 AM
ramdrop
Re: Laplace transforms? Inverse?
You're right, I missed out the first part..

t f ''(x) + (1-t)f ' (x) +nf = 0

You first had to take the laplace transform of that and prove L(t) above, which i did., now I need to do t L(t), I presume you times this by t and do the same process?
• Mar 8th 2012, 03:29 PM
Issler
Re: Laplace transforms? Inverse?
what you're calling L(t) has no t in it...
plus what do you mean by f(x)?
I assume you mean f(t) instead?
think about what you're going to say and I might help (Nerd)
• Mar 13th 2012, 08:04 PM
Kiwi_Dave
Re: Laplace transforms? Inverse?
if F(s) is the laplace transform of f(t) then there is an identity that says:

the laplace transform of t*f(t) is -F'(s)

using this identity and the integral definition of the laplace transform (with s=2) I think you should be able to solve your problem. That is if I have guessed the problem correctly.