Solving a differential equation - logistic model with harvesting I have the differential equation
$$\frac{\mathrm dP}{\mathrm dt}=\frac{2}{25}P(t) \left (1-\frac{P(t)}{1000}\right)-15$$
which I was able to rearrange and integrated using partial fractions
$$\int \left(\dfrac{25}{p-250} - \dfrac{25}{p-750}\right)\,\mathrm dP=\int1\,\mathrm dt$$
but once I integrated I tried rearranging to solve for p but got stuck with the below
$$\frac{p-250}{p-750}=(e^t +e^c)^{1/25}$$

$$e^{(t+c)/25}=e^{t/25}·e^{c/25}=C·e^{t/25},$$ the negative constants are possible as the anti-derivative of $\frac1u$ is $\ln|u|$ so that the left side of the last equation can also be negative.
You get the solution faster by dividing the original equation by $P^2$ and substituting $Q=\frac1P$.
