Here's the problem:
y'''(x) = f(x) subject to the conditions y(0)=y(1)=y(2)=0.
Perform three integrations to show that a solution may be written
After triple integration I get
where A and B are constants which I've determined but won't write here.
Anyway, I don't see how this can be converted to find the desired L(x,t)
(I'm assuming my triple integration is correct- I think it is)