An integral equation of the second kind
Fredholm integral equations of the second kind are of the form
where the kernel 
and data 
are given, and the problem is to find 
. Sometimes solutions exist and are unique, but that’s not guaranteed.
But you don’t need to know anything about IEs to solve this problem:
Give it a try!
Bonus! solve this one:
I was surprised that it’s relatively easy to get this solution in a closed form. There’s a trick to it…
Possibly relevant posts:
- Eikonal equation (11/14/2006)
- Systems of Sets (10/7/2005)
- Exactness of differential forms (7/28/2007)