Chapter 2.2, Problem 19P

Program Plan Intro

Program Description:Purpose ofproblem is to calculate the dependence of the number of critical points on the parameter $h$ of the differential equation $\frac{dx}{dt}=\frac{1}{10}x\left(10-x\right)-h$ and then construct the bifurcation diagram.

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.