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

$y=xf(p)+g(p)$

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.