Series Solutions of the Anharmonic Motion Equation y" + y2 = C

Abstract

Among equations representing motion of a mass or a particle in physics, many of them are anharmonic and consist of one or more nonlinear terms. This article shows how to obtain series solutions of the equation of the form which is an anharmonic motion equation. The authors focus the effort on the case with constant and make use of the Taylor's series method; this sets the article apart from those of other authors who did similar works in the past. The series solution obtained under the indicated conditions is of the form which does not appear very often in general mathematical functions.