In mathematical analysis, Clairaut's equation is a differential equation of the form {\displaystyle y(x)=x{\frac {dy}{dx}}+f\left} where f is continuously differentiable. It is a particular case of the Lagrange differential equation.

How do you solve clairaut's equation?

y(x)=Cx+f(C), the so-called general solution of Clairaut's equation. y=xy′+(y′).

Is clairaut's equation linear?

An ordinary first-order differential equation not solved with respect to its derivative: y=xy′+f(y′), where f(t) is a non-linear function.