I would like to know the analytical solution of the following ODE.
[Hutchinson's Equation]
$N'(t)=rN(t)(1-\frac{N(t-\tau)}{K})$
Where $r> 0$ is the intrinsic growth rate of the species and $K> 0$ is the persistence capacity or carrying capacity for said species.
This formula comes from the Verhulst logistic equation whose form is.
[Verhulst Logistic Equation]
$N'(t)=rN(t)(1-\frac{N(t)}{K})$
Only that Hutchinson's equation considers tau "$\tau$" as the retarder (delay or lag)
What would be the solution of the Hutchinson's equation?