How can I solve this rather simple looking integral equation? I was working on a physics problem and I have reduced it down to a simple integral equation with two boundary conditions:
$$\int_0^{l-t}y(x, t) dx = lh$$
With the conditions:
$$y(0, t) = y(l-t, t) = h$$
I am looking for $y(x, t)$. $l$, $h$ and $t$ are positive real numbers.
Unfortunately, I don't know how to solve it. So, I need a little help there.
Also, I am curious if this same problem could be converted into a differential equation.

Has this something to do with FEM?
I would do: 
at $x=0$, $$y(x, t)=h$$
at $x=\frac{1}{2} \cdot(l-t)$, $$y(x, t)=h+\frac{2ht}{l-t}$$
at $x=(l-t)$, $$y(x, t)=h$$
Is this what you are looking for?
