ABSTRACT
A differential equation is an equation relating some function f to one or more of its derivatives. Many of the laws of nature—in physics, in engineering, in chemistry, in biology, and in astronomy—find their most natural expression in the language of differential equations. Certainly Newton’s law of universal gravitation, Maxwell’s field equations, the motions of the planets, and the refraction of light are important examples that can be expressed using differential equations. Many of the special curves of classical mathematics arise in problems of mechanics. The tautochrone property of the cycloid curve was discovered by the great Dutch scientist Chris-tiaan Huygens. He published it in 1673 in his treatise on the theory of pendulum clocks, and it was well-known to all European mathematicians at the end of the seventeenth century.
