Clairaut's equation

In mathematical analysis, Clairaut's equation (or the Clairaut equation) is a differential equation of the form

${\displaystyle y(x)=x{\frac {dy}{dx}}+f\left({\frac {dy}{dx}}\right)}$

where ${\displaystyle f}$ is continuously differentiable. It is a particular case of the Lagrange differential equation. It is named after the French mathematician Alexis Clairaut, who introduced it in 1734.^[1]