D'Alembert's equation

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


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

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


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

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