From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!

# Differential Equations and Their Solutions

A differential equation (d.e.) is any equation that has one or more derivative in it. These can be first derivatives, second derivatives...whatever.

### Sample Problem

The following are differential equations.

' + " + xy = 0

### Sample Problem

The following are not differential equations, because they don't contain any derivatives.

x2 + y2 = 8

x + xy – y + 9 = 0

x = 9

The order of a differential equation is the highest derivative that occurs in that differential equation.

### Sample Problem

The differential equation

' + " + "' + x = 0

has order 3 because that's the highest derivative in the equation:

' + " + "' + x = 0.

### Sample Problem

The differential equation

has order 1 because it only contains a first derivative.

A d.e. of order 1 is called a first-order differential equation, and a d.e. of order 2 is called a second-order differential equation. These are the kinds of differential equations that you'll probably see most often.