ABSTRACT
Second-order linear equations are important because they arise frequently in engineering and physics. For instance, acceleration is given by the second derivative, and force is mass times acceleration. This chapter deals with a last example of a homogeneous, second-order, linear ordinary differential equation with constant coefficients and with complex roots, just to show how straightforward the methodology really is. Newton’s second law of motion says that the mass of the cart times its acceleration equals the force acting on the cart. The analogy between the mechanical and electrical systems renders identical the mathematical analysis of the two systems, and enables us to carry over at once all mathematical conclusions from the first to the second. Newton’s derivation of Kepler’s laws, presented in a modernized and streamlined form, is a model for the way that mathematical physics is done.
