Chapter 2.2, Problem 24P

Program Plan Intro

Program Description: Purpose of problem is to find the solution of the logistic equation $\frac{dx}{dt}=k\left(N-x\right)\left(x-H\right)$ .

Summary introduction:

Problem will use the separation of the variable for differential equation $\frac{dy}{dx}=f\left(x\right)g\left(y\right)$ and the integral of $x^{-1}$ can be calculated as ${\displaystyle \int \frac{1}{x}dx=\ln \left|x\right|+c}$ where $c$ is called the constant of integration.