I'm more concerned with the general question of whether any function satisfies the differential equation $f'(x) = f(x+a)$, $a \in \mathbb{R}$. I've tried solving it myself, to no avail.
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2This is a simple type of Delay Differential Equation. It's possible to find non-zero solutions by trying solutions of the form $e^{\lambda x}$. Finding $\lambda$ involves the Lambert W function. – Theo Bendit Mar 26 '21 at 06:02
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Thank you so much! – Rowaaaan Mar 26 '21 at 06:05