In mathematics, d'Alembert's equation is a first order nonlinear

ordinary differential equation In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contras ...

, named after the French mathematician

Jean le Rond d'Alembert Jean-Baptiste le Rond d'Alembert (; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the '' Encyclop� ...

. The equation reads asDavis, Harold Thayer. Introduction to nonlinear differential and integral equations. Courier Corporation, 1962. :

y = x f(p) + g(p)

where

p=dy/dx

. After differentiating once, and rearranging we have :

\frac + \frac=0

The above equation is linear. When

f(p)=p

, d'Alembert's equation is reduced to

Clairaut's equation In mathematical analysis, Clairaut's equation (or the Clairaut equation) is a differential equation of the form :y(x)=x\frac+f\left(\frac\right) where ''f'' is continuously differentiable. It is a particular case of the Lagrange differential eq ...

References

Equations of physics Mathematical physics Differential equations Ordinary differential equations {{Mathanalysis-stub