Thread: 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.

this question doesn't make any sense
rephrase it and then I might be able to help you

You're right, I missed out the first part..

We start with the differential equation.

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?

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

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.