# Solving a Logistic model equation with harvesting

I have the following Logistic model equation (left out the values for the constants for simplicity), which I'm unable to solve for $P(t)$.

$\dfrac {dP} {dt} = kP \left (1- \dfrac P {P_\infty} \right)-H$

If the harvesting constant, $H$ was not present, then the ODE could be solved by Bernoulli's equation. The problem is that I am not sure how to start solving this specific type of differential equation.

Can someone point me in the right direction?

The equation is in separated variables: $$\frac{dP}{k\,P \left (1- \dfrac P {P_\infty} \right)-H}=dt.$$

• Ah I see. But that looks like a beast to solve right? What would be your first step if you went this route? Thanks for the reply! – KidMe Mar 10 '15 at 21:24
• It is polynomial in the denominator of degree two. Parcial fraction descomposition. – Julián Aguirre Mar 10 '15 at 23:55
• Partial fractions? How would you start doing that, since you don't have 2 factors in the denominator. Thanks for the reply! – KidMe Mar 11 '15 at 12:14
• You are supposed to find the factors. – Julián Aguirre Mar 11 '15 at 12:29
• Thank you Julián for the help. I had managed to work it out in the end! – KidMe Mar 18 '15 at 17:59