I tried to solve the integral equation
$$f(x) \int_a^x \int_a^{t} f(\omega) d\omega dt - \left[ \int_a^x f(t) dt \right]^2 = 0$$
by taking the first, second, third, and fourth order derivatives but I ended up with an expression that was much more complicated than the original expression. Why the fourth derivative? That's simply where I gave up on expanding the product rule on a piece of paper.
How do I go about finding a function $f$ that satisfies the integral equation?