D'Alembert equation

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A differential equation of the form


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


For $\phi(y')=y'$ 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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This article was adapted from an original article by BSE-2 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article