Graphic Solution of a First-Order Differential Equation

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration presents Euler's method for the approximate (or graphics) solution of a first-order differential equation with initial condition , .


The method consists of calculating the approximation of by



where .

These coordinates determine points , , …, . These points form Euler's polygonal line that is an approximate solution of the problem. The Demonstration compares it with a better solution provided by Mathematica's built-in NDSolve function (brown line).


Contributed by: Izidor Hafner (January 2014)
Open content licensed under CC BY-NC-SA




[1] L. Euler, "De Integratione Aequationum Differentialium Per Approximationem," Institutionum Calculi Integralis Volumen Primum, 1768.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.