Solving Differential Equation w/ Laplace Transform

[Neoon]

Hi all,

Just a small question:
I came across a problem to solve a differential equation using Laplace transform.

I solved the major part but only still a part where I had to inverse transform the following experssion:

(exp(-s))/(s^2)

I looked in Laplace Transform Tables but did not find it.

Could you please help?

 

[tpm]

think i got it..

you're looking for the integral..

(2\pi i)^{-1} \oint ds exp(-st-s)/s^{2}

now using 'Residue theorem' you get...

f(t)=0 iff t<1 and f(t)=t/2 [/tex] iff t>1.


depending on if you take the semi-circle (-T,0) or (0,T) with T--->oo , there is a double pole at s=0