I have a differential equation (Or integral equation) of the form:
$$ f(x) = a e^{-x} + b \int_0^x f(cz+dx) e^{-z} dz$$
$a,b,c,d$ are constants.
I am considering whether the above equation has a closed form solution. If not, why it is the case? If so, I think guessing a functional form and using method of undetermined coefficients. But I am not sure how to guess.
Thanks so much!