Clairaut’s Equation

Clairaut’s equation, in mathematics, a differential equation of the form y = x (dy/dx) + f(dy/dx) where f(dy/dx) is a function of dy/dx only. The equation is named for the 18th-century French mathematician and physicist Alexis-Claude Clairaut, who devised it. In 1736, together with Pierre-Louis de Maupertuis, he took part in an expedition to Lapland that was undertaken for the purpose of estimating a degree of the meridian, and on his return he published his treatise Théorie de la figure de la terre (1743; “Theory of the Shape of the Earth”). In this work he promulgated the theorem, which connects the gravity at points on the surface of a rotating ellipsoid with the compression and the centrifugal force at the Equator.