D'Alembert's equation

In mathematics, d'Alembert's equation is a first order nonlinear ordinary differential equation, named after the French mathematician Jean le Rond d'Alembert. The equation reads as[1]

y=xf(p)+g(p)

where $p=dy/dx$ . After differentiating once, and rearranging we have

{\frac {dx}{dp}}+{\frac {xf'(p)+g'(p)}{f(p)-p}}=0

The above equation is linear. When $f(p)=p$ , d'Alembert's equation is reduced to Clairaut's equation.

References

Davis, Harold Thayer. Introduction to nonlinear differential and integral equations. Courier Corporation, 1962.

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