I try to solve for the specific function $f(x) = \frac{2-2a}{x-1} \int_0^{x-1} f(y) dy + af(x-1)$
It looks similar to the function used to find the Renyi's parking constant because it came out from a simple generalization of that problem.
The skill I have gained in my differential class can't even solve $f(x) = f'(x-1)$
I'm not looking for anyone to solve it. I just want to know the techniques for solving DE where functions and it's derivatives are evaluated at different points.(What's the terminology for this kind of DE?)