ABSTRACT
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. Put in other words, differential equations are the language of nature. Certainly Newton’s law of universal gravitation, Maxwell’s field equations, the motions of the planets, and the refraction of light are important examples which can be expressed using differential equations. The chapter looks at two very simple examples to get a notion of what solutions to ordinary differential equations look like. For a large class of equations, a number of “independent” solutions can be found equal to the order of the differential equation. Then, a so-called “general solution” can be formed by combining them. The chapter considers the first general class of equations which are the class of separable equations. Another class of differential equations that is easily recognized and readily solved, is that of first-order, linear equations.
