I have the following different equation
$$f'(x) = f(x/2)$$
What type of DE is this, and how would you solve it?
It seems $f(x)$ is likely to be some relative of $e^x$, since $f'(x) = f(x)$, which is close, but I don't even know what that type of DE is called with that $f(x/2)$ feature, so I'm not having any luck searching for a tutorial. The best candidate I've found was a "delay differential equation", but that seems more suited to $f(x-3)$ than $f(x/2)$.