This section deals with one of the best applications of calculus, to the area of differential equations . Many differential equations come from modeling some sort of natural process, such as Newton's second law, stating that the acceleration of a body will be proportional to the force acting upon it. A solution to that equation will express the velocity directly in terms of time, which can easily be integrated to get the position as a function of time. There are a number of different techniques for solving differential equations.
Complicated equations require subtle techniques.
It may seem at times that the subject of differential equations is just a collection of tricks to solve specific equations. Today we will just work out the solution to one differential equation, which will be applied to a number of problems. Because most of the applications will deal with time, we will assume that the variable is time, t .