A population of fish that's growing is harvest at a rate of $k$, from $t = 0$ to $t = T$ and follows the DE:
$$DP/dt = P + k(H(t-T)-1), \qquad P>0$$
How do I solve the IVP with $P(0) = P_0> 0$? What's confusing me is the Heaviside function $H(t-T)$. I don't know what to do with it.