# The Murder Mystery Method for Identifying and Solving Exact Differential Equations

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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 .

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Contributed by: José Luis Gómez-Muñoz, Roxana Ramírez-Herrera, Jezahel Lara-Sandoval, and Edgar Fernández-Vergara (March 2011)

Open content licensed under CC BY-NC-SA

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## Details

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.