Solve the following integral equation
$ u(x)= \cos x - \int_{0}^{x} (x-y)cos(x-y)u(y) dy $
I applied Laplace transforms to the above integral equation and so the initial equation is written as:
$ U(s)= \frac{s}{s^2+1} - \frac{(s^2 -1)U(s)}{(s^2+1)^2} $
and then I concluded to this : $U(s)= \frac{s^2+1}{s(s^2+3)} $ .
At this point I've been stuck. I can't find the function $u(x)$ whose laplace transform is the above... I would appreciate any help!!!!!
Thanks in advance!!