Loop differential equation involving latency

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I am trying to find out what the solution is for the following differential equation:

y'(t) = K y(t-a)

where K is a constant and a is a latency parameter.

This equation describes a positive feedback loop in time after an a latency.

So far, I know that for no latency, a=0, the equation has an exponential solution like this

y(t) = exp(Kt + C1)

where

C1 = ln(y(0))

Thank you in advance.