Rubel (1981) found the first known UDE by showing that, given any continuous function
and any positive continuous function , there exists a solution of

(1)

such that

(2)

for all .

Duffin (1981) found two additional families of UDEs,

(3)

and

(4)

whose solutions are for .

Briggs (2002) found a further family of UDEs given by

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