# 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..

### Pendulum

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.