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

y(x) = $\displaystyle \int_{0}^{2}L(x,t)f(t)dt$

Determine L(x,t).

My attempt:

After triple integration I get

y(x) = $\displaystyle Ax +Bx^2 +\frac{1}{2}\int_{0}^{x}(x-t)^2f(t)dt$

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)