d'Alembert's equation
From HandWiki
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]
- [math]\displaystyle{ y = x f(p) + g(p) }[/math]
where [math]\displaystyle{ p=dy/dx }[/math]. After differentiating once, and rearranging we have
- [math]\displaystyle{ \frac{dx}{dp} + \frac{x f'(p) + g'(p)}{f(p)-p}=0 }[/math]
The above equation is linear. When [math]\displaystyle{ f(p)=p }[/math], 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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