d'Alembert's equation

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In mathematics, d'Alembert's equation, sometimes also known as Lagrange's equation,[1] is a first order nonlinear ordinary differential equation, named after the French mathematician Jean le Rond d'Alembert. The equation reads as[2]

where . After differentiating once, and rearranging we have

The above equation is linear. When , d'Alembert's equation is reduced to Clairaut's equation.

References

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  1. ^ Weisstein, Eric W. "d'Alembert's Equation". mathworld.wolfram.com. Retrieved 2024-06-02.
  2. ^ Davis, Harold Thayer. Introduction to nonlinear differential and integral equations. Courier Corporation, 1962.