This is my first attempt at an integral equation so I don't really know what's going on.

Suppose that y = y(x) satisfies the integral equation

Find .

I've split the integral at t = x to get:

Using Leibnitz's integral rule, differentiating once gives:

So

Differentiating again,

So now everything cancels?

I know the answer is but I just can't see how to get there from here...

Thanks in advance for any help, I've literally been working on this for days!