Question

How do I integrate the differential form of the logistic equation? I'm just confused by all of the different variables that people use for this equation.

Answer 1

\[dN/dt=RN((k-N)/k)\]
I know that this is separable.

Answer 2

\[\frac{\text dN}{\text d t}=RN\left(\frac{k-N}k\right)\]
\[\frac{k\cdot\text dN}{N(k-N)}= R\cdot{\text d t}\]
\[\int\frac{k\cdot\text dN}{N(k-N)}= \int R\cdot{\text d t}\]