Ordinary Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives. These videos cover topics important in understanding and solving first- and second-order differential equations.

Preview differentiation

This university preview discusses the concept of a differential equation: an equation that expresses a relationship between an unknown function and its derivatives. The example of a cooling coffee cup is used to find the differential equation and solve it using differentiation.

Direction Field

What is a direction field? A direction field helps you to get an impression of the solutions to a differential equation. In this video you will learn how to draw a direction field.

Searching for solutions

How do you find the solution to a differential equation? Sometimes you can guess a solution. In this video you learn how to do that.

The integrating factor

In this video you will learn the form of a first-order linear differential equation and learn to solve these linear differential equations with the use of the integrating factor.

Separable differential equations

What are separable differential equations? In this video you will learn what they are and how to solve them. 

First Order Linear Differential Equations

Some linear differential equations are easier to solve than others. This video explains the integrating factor, which can help when solving linear differential equations..


To derive the Differential Equation of a swinging pendulum Newton's law is used. The resulting second order differential equation is non-linear. To solve it, you can use linearisation .

Second-order differential equations

How to solve the differential equation associated to a mass at the end of a vibrating spring? This is a second order differential equation.

Solving nonhomogeneous second-order differential equations

How to solve a second-order nonhomogeneous linear differential equation with constant coefficients? The example of a mass at the end of a vibrating string is used taking into account spring force, damping force and an external force.