A Solution of Euler's Type for an Exact Differential Equation

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

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

An equation of the form is the general solution of the exact differential equation (or ). So the contours of the Mathematica built-in function ContourPlot are particular solutions of the equation. To find a graphical solution (of Euler type) of the equation, choose an initial point using the locator, the length of the tangent, and then proceed along the green arrow and add new locators. The green arrow is perpendicular to the red arrow that shows the direction of the gradient. Check the solution by increasing the number of contours. To construct Euler's polygonal line, choose a sufficiently long tangent line and the step given by vertical mesh lines.


The choices for the function are:

(1) ,

(2) ,

(3) .


Contributed by: Izidor Hafner (March 2011)
Open content licensed under CC BY-NC-SA



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.