The number, $N$, of animals of a certain species at time $t$ years increases at a rate of $aN$ per year by births, but decreases at a rate of $\mu t$ per year by deaths, where $a$ and $\mu$ are positive constants.
Modelled as continuous variables, $N$ and $t$ are related by the differential equation: $dN/dt=aN-\mu t$
Given that $N=N(0)$ when $t=0$, find $N$ in terms of $t$, $a$, $\mu$ and $N(0)$.