integral equation by Laplace transforms and contour integration

i have to solve by using Laplace transforms and then inverting it using contour integration (which i'm incredibly vague on)

we were given the rule that if then , and also that the Laplace transform of an integral is

i found the Laplace transform of is and of is

do i have to Laplace transform the integral on the left as well? or do I multiply both Laplace transforms together and then integrate by contour integration?

i'm a little confused as to what to do next!

Re: integral equation by Laplace transforms and contour integration

Quote:

Originally Posted by

**wik_chick88** i have to solve

by using Laplace transforms and then inverting it using contour integration (which i'm incredibly vague on)

we were given the rule that if

then

, and also that the Laplace transform of an integral is

i found the Laplace transform of

is

and of

is

do i have to Laplace transform the integral on the left as well? or do I multiply both Laplace transforms together and then integrate by contour integration?

i'm a little confused as to what to do next!

Take the LT of your integal equaltion:

where

CB

Re: integral equation by Laplace transforms and contour integration

so am I solving for ? ie. i find the Laplace transform of and sub that and also my Laplace transforms of and into the equation, simplify and then inverse Laplace transform to get ?

Yes.

CB