Clairaut's Equation

Any differential equation of the form
$y = px + f(p)$ where $p= \frac{dy}{dx}$ and y is a function of x is known as Clairaut's Equation.
named after Alexis Claude de Clairaut, a French mathematician.

The simplest Solution of this type of equation is
$y = cx + f(c)$ where c is any arbitrary constant.

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