Assume we want to find the following integration:

\begin{equation}\int_{t=0}^{\infty} p(t)dt\end{equation}

where $p(0)=p$ and also $$\frac{dp(t)}{dt}=-p(t)(1-p(t))\mu$$.

Is there any easy way to exploit the second equation and calculate the first integration?

Any comment is highly appreciated.

  • 2
    $\begingroup$ See the logistic model. $\endgroup$ – Git Gud Apr 21 '14 at 21:14
  • 2
    $\begingroup$ You have the ODE $\dot p=\mu p(p-1)$, thus $p=\frac{\dot p}{\mu(p-1)}$. $\endgroup$ – David H Apr 21 '14 at 21:18

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