A note on Chrystal's equation

doi:10.1016/j.amc.2010.05.095

A note on Chrystal's equation

2010-09-01

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P.M. Jordan *

DOI：10.1016/j.amc.2010.05.095

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The exact, explicit form of the transcendental solution of Chrystal's equation, a first order nonlinear ordinary differential equation (ODE) of degree two, is derived in terms of the Lambert W-function. It is shown that this case of the general solution is dual-valued over a finite interval and that, for a special case of the coefficients, its zeros involve the Golden ratio. Additionally, a number of applications involving special cases of this ODE are noted and the main properties of the Lambert W-function are briefly reviewed. Published by Elsevier Inc.

Keyword:

Chrystal's equation

Nonlinear ordinary differential equations

Lambert W-function

Golden ratio

A note on Chrystal's equation

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