Difference between revisions of "D'Alembert equation"
From Encyclopedia of Mathematics
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$$y=x\phi(y')+f(y'),$$ | $$y=x\phi(y')+f(y'),$$ | ||
| − | where $\phi$ and $f$ are the functions to be differentiated; first studied in 1748 by J. d'Alembert. Also known as the Lagrange equation. | + | 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. |
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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]]]. | 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==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> E.L. Ince, "Integration of ordinary differential equations" , Oliver & Boyd (1963) pp. | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> E.L. Ince, "Integration of ordinary differential equations" , Oliver & Boyd (1963) pp. 43 {{ZBL}0612.34002}}</TD></TR> | ||
| + | </table> | ||
Latest revision as of 11:24, 22 March 2023
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.
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. 43 {{ZBL}0612.34002}} |
How to Cite This Entry:
D'Alembert equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=D%27Alembert_equation&oldid=32805
D'Alembert equation. Encyclopedia of Mathematics. URL: http://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