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What do you think about the possible (nontrivial) solutions of this equation ?

(1) f '(x) = f(x-1) (f is a smooth function R -> R)

More generally, what do we know about these ?

(2) f '(x) = f(x+a) (a fixed in R)

(3) f '(x) = f(g(x)) (g smooth diffeomorphism R -> R )

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# A strange, but very simple, differential equation

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