The Logistic Differential Equation for Population Growth: General Solution

In this video, we work through the process for deriving the analytical solution to the Logistic Equation formulated by Verhulst for modelling population growth.
We first compare the natural (exponential) and logistic models and their formulas.
The logistic equation is given by:
dP/dt = rP [1 - K/P]
This is a separable differential equation with which we can separate the variables and solve by integration.
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[@ambikamohta8753]

amazingly explained! would be beneficial if you could upload more mathematical videos as in related to subjects like bioprocess, applied physics in biology . thank you

[@icee562]

Thanks for an awesome explanation both qualitatively and quantitatively.

[@markgorman3842]

Thanks very much. That was really clear.

[@sohaibaziz2068]

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[@nabuulekevin8023]

why does the logistic equation appear the way it is?

[@MasterWuMathematics]

I'm not aware of a proof for the logistic differential equation when it comes to modelling population growth. It may have been formulated by observation and deduction by the likes of Verhulst and Pearl circa. 1920.