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.