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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?

Thank you for your time!

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

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  • $\begingroup$ 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! $\endgroup$ – KidMe Mar 10 '15 at 21:24
  • $\begingroup$ It is polynomial in the denominator of degree two. Parcial fraction descomposition. $\endgroup$ – Julián Aguirre Mar 10 '15 at 23:55
  • $\begingroup$ Partial fractions? How would you start doing that, since you don't have 2 factors in the denominator. Thanks for the reply! $\endgroup$ – KidMe Mar 11 '15 at 12:14
  • $\begingroup$ You are supposed to find the factors. $\endgroup$ – Julián Aguirre Mar 11 '15 at 12:29
  • $\begingroup$ Thank you Julián for the help. I had managed to work it out in the end! $\endgroup$ – KidMe Mar 18 '15 at 17:59

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