About this course

This site is a free, self-contained course on ordinary differential equations, written for engineering and science students taking their first course on the subject. It follows the standard syllabus of such a course: first-order equations and their applications, higher-order linear equations, vibrations and circuits, series solutions, systems, numerical methods and the Laplace transform.

How the material is written

Simple language. Each idea is explained in plain words before any formula appears.
Small steps. Derivations are shown line by line, without skipping the algebra.
Original examples. All worked examples and exercises were created for this site, and every answer has been checked with computer algebra.
Interactive solvers. For each method there is a tool that solves your equation and shows every step. All computations use exact arithmetic and run in your browser.
Chapter quizzes. Every chapter ends with a quiz that creates four new problems each time it runs.

Prerequisites

Single-variable calculus (derivatives, integrals, integration by parts, partial fractions) and basic algebra. Some sections use complex numbers and matrices; short reminders are given where they are needed.

Free to use

The site is free to use, with no sign-up, no advertisements and no tracking.

Copyright

All text, explanations, worked examples, exercises and solutions, figures, quizzes and interactive solvers on this site are original works owned by differential-equations.com and are protected by copyright.

Permitted: reading and using the material for your own personal, non-commercial study, printing pages for that purpose, and linking to any page of the site (teachers are welcome to point students to it).
Short quotations for teaching, study or review are permitted when the source is clearly acknowledged as "differential-equations.com" with a link to the page quoted.
Not permitted without prior written permission: copying, reproducing, redistributing, translating, adapting or republishing any part of the site, in print or electronically, including on other websites, in course packs, in apps or as training data.

Names of mathematical methods and theorems (Euler, Bernoulli, Laplace, Bessel and others) are used in their standard scientific sense. Any third-party trademarks mentioned remain the property of their owners.