View source for 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 [[DAlembert|J. d'Alembert]]. Also known as the Lagrange equation.

For $\phi(y')=y'$ the d'Alembert equation specializes to the [[Clairaut equation|Clairaut equation]]. For some results on (solving) the d'Alembert equation cf., e.g., [[#References|[a1]]].

====References====
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  E.L. Ince,   "Integration of ordinary differential equations" , Oliver &amp; Boyd  (1963)  pp. 43 {{ZBL}0612.34002}}</TD></TR>
</table>