The Murder Mystery Method for Identifying and Solving Exact Differential Equations

Finding out whether a first-order differential equation is exact or not is solving a little "mystery": Is there a function such that its differential change is precisely ? If the answer is "yes", then the equation implies that the change of the function is zero, and therefore the function is equal to a constant,. This last equality is actually an implicit solution of the differential equation .
Tevian Dray and Corinne A. Manogue designed a fun and engaging way to explain how to solve these kind of "mysteries": A crime has been committed (the differential equation), and the student is the detective who must identify the murderer . The detective interrogates (integrates) the witnesses ( and ). If the clues given by them are consistent, then the murderer can be identified (therefore the implicit solution to the differential equation is obtained). If the clues are not consistent, the equation is not exact and has to be solved by another method.
Use the popup menus of this Demonstration to generate different differential equations and see this "Murder Mystery Method" applied to them. Pay attention to the colors and labels of the murderer's clothes and the mathematical expressions, as they show the relationship between the "murder" story and the mathematical procedure.
Elementary my dear Watson!


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Tevian Dray and Corinne A. Manogue designed their "Murder Mystery Method" (MMM) in order to determine whether a vector field is conservative or not. The authors of this Demonstration adapted this method to the solution of exact differential equations.
The original authors of the MMM emphasize that "... if two witnesses say they saw someone with red hair, that doesn't mean the suspect has two red hairs! So if you get the same clue more than once, you only count it once..."
T. Dray and C. A. Manogue, "The Murder Mystery Method for Determining Whether a Vector Field Is Conservative," The College Mathematics Journal, 34(3), 2003 pp. 228–231.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+