Sections 10.1 and 10.2

Main Points: Differential equations are made from information we know, such as the derivative or the rate of change and are used to find an unknown value. This is useful for finding the net worth of a company or the rate of change in a population. Differential equations involve the derivative of an unknown function. A solution to a differential equation is any function that satisfies the differential equation. These sections also talk about finding an unknown constant in a differential equation. The general solution is a family of functions while a particular solution is one for a specified value. The differential equation and the initial condition together are called an initial-value problem.

Challenges: Some students may have found the idea of finding the unknown constant challenging since it involves more information. Also, creating a differential equation is a bit difficult because you have to know exactly which information goes where in the differential equation.

Reflections: Differential equations are super helpful in the real world. Finding the net worth of a company or increases or decreases in population growth are important values to know, especially for other companies or projects, etc.