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 , .

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).