Differential Equations

What is a differential equation?

A differential equation contains one or more terms involving derivatives of one variable (the dependent variable, y) with respect to another variable (the independent variable, x).

For example,

What does the solutions of a differential equation look like?

Unlike algebraic equations, the solutions of differential equations are functions and not just numbers.

What exactly does a differential equation represent?

It represents the relationship between a continuously varying quantity and its rate of change. This is very essential in all scientific investigation.

Where are differential equations used in real life?

In physics, chemistry, biology and other areas of natural science, as well as areas such as engineering and economics.

This is a picture of wind engineering.

What is an ordinary differential equation?

A differential equation that involves a function of a single variable and some of its derivatives.

For example,

What is the order of a differential equation?

The order of a differential equation is the order of the highest derivative that appears in the equation. The above examples are both first order differential equations.

An example of a second order differential equation is .

Explore & Experiment