We study a special type of differential equation.

A differential equation is simply an equation with a derivative in it like this: When a mathematician solves a differential equation, they are finding a function that satisfies the equation.

Consider a falling object. Recall that the acceleration due to gravity is about m/s. Since the first derivative of the velocity function is the acceleration and the second derivative of a position function is the acceleration, we have the differential equations

From these simple equations, we can derive expressions for the velocity and for the position of the object using antiderivatives.

Now let’s do a similar problem, but instead of finding the velocity, we will find the position.

The power of calculus is that it frees us from rote memorization of formulas and enables us to derive what we need.