Differential Equations

Solving an equation in a math class usually involves an unknown number, x. The equation hides the value but gives you hints as to how to find the value, such as . But to solve a differential equation, you're only given information regarding the derivative of a function, and you're expected to find the function. It could be something as simple as the following:

Figure 12.1: Finding a function with derivative 2

This means find a function whose derivative is 2. This can also be written as follows:

Figure 12.2: Alternative way to represent derivative of the function

By simple integration, we can find functions that work in this equation because we know the function y = 2x has a derivative of 2. In fact, many related functions, such as y = 2x + 1, y = 2x + 2, y = 2x + 3, and so on, all have a derivative of 2. So, we write a general form, that is, y = 2x + C.

Things get more complicated when we don&apos...