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D'Alembert equation

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A differential equation of the form

$$y=x\phi(y')+f(y'),$$

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


Comments

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].

References

[a1] E.L. Ince, "Integration of ordinary differential equations" , Oliver & Boyd (1963) pp. 43ff
How to Cite This Entry:
D'Alembert equation. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=D%27Alembert_equation&oldid=32805
This article was adapted from an original article by BSE-2 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article