# Differential equations/Ordinary Differential Equations

**Work in progress**

For engineers and scientists, your introduction to a differential equation probably occurred in your Calculus I class, where you were introduced to the derivative of a function (i.e. . At the same time you were taking introductory physics where concepts such as Newton's second law of motion (for linear motion) was presented as , and when combined with led to the differential equation , .

Similarly many fundamental laws of science are expressed as differential equations:

- Law of Conservation of Mass: Rate of Mass In - Rate of Mass Out = Rate of Change of Mass content
- Law of Conservation of Energy: Rate of Energy In - Rate of Energy Out = Rate of Change of Energy content

Each of these represents the change in a quantity (dependent variable) with respect to an independent variable (such as time).

- Law of Conservation of Mass: Rate of Mass In - Rate of Mass Out = Rate of Change of Mass content,

An nth order differential equation is of the form ). For example, when Newton's second law of motion, , is applied to a moving object the resulting differential equation is