Graphic Solution of a First-Order Differential Equation
This Demonstration presents Euler's method for the approximate (or graphics) solution of a first-order differential equation with initial condition , .[more]
The method consists of calculating the approximation of by
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).[less]
 L. Euler, "De Integratione Aequationum Differentialium Per Approximationem," Institutionum Calculi Integralis Volumen Primum, 1768. www.math.dartmouth.edu/~euler/docs/originals/E342sec2ch7.pdf.