# D'Alembert equation

From Encyclopedia of Mathematics

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