D'Alembert equation

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A differential equation of the form

where and are the functions to be differentiated; first studied in 1748 by J. d'Alembert. Also known as the Lagrange equation.


For the d'Alembert equation specializes to the Clairaut equation. For some results on (solving) the d'Alembert equation cf., e.g., [a1].


[a1] E.L. Ince, "Integration of ordinary differential equations" , Oliver & Boyd (1963) pp. 43ff
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D'Alembert equation. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by BSE-2 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article