McLachlan N.W. Ordinary Non-Linear Differential Equations in Engineering and Physical Sciences

Oxford At the Clarendon Press, 1950. - 201 Pages.In the so-called classical theories of different branches of science the differential equations are mainly linear in type. They have been the subject of intense study, and the existence of well-known forms of solutions is now established beyond doubt. If anyone skilled in mathematical analysis encounters a linear differential equation of standard type, the formal solution is usually not difficult to obtain.
The comparatively simple nature of such equations is due to the 'characteristic' relationships of the systems, which they describe symbolically, being assumed to be linear. For instance the characteristic relationship used in developing the theory of sound propagation.