View source for D'Alembert equation

A differential equation of the form

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d030/d030040/d0300401.png" /></td> </tr></table>

where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d030/d030040/d0300402.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d030/d030040/d0300403.png" /> are the functions to be differentiated; first studied in 1748 by J. d'Alembert. Also known as the Lagrange equation.



====Comments====
For <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d030/d030040/d0300404.png" /> 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====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  E.L. Ince,   "Integration of ordinary differential equations" , Oliver &amp; Boyd  (1963)  pp. 43ff</TD></TR></table>