ON APPLICATION OF THE METHOD OF SEPARATION OF VARIABLES TO FIND SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS

Abstract

This work is devoted to a very topical issue for those engaged in mathematical physics-some aspects of the method of solving nonlinear differential equations. Almost always, when studying natural and creating technological processes, it is necessary to create their technological models, and they, in turn, almost always lead to the creation of differential equations and, of course, to the need to find their solution, if possible, accurate. We consider the method of application of the most commonly used method of solving differential equations - the method of separation of variables. The novelty of this work is that the analysis of the application of the method, in fact, engaged in a little. The problem is that for nonlinear differential equations, which are usually the final result of modeling the process, the solution by the method of separating variables looks quite different than for linear equations, much more difficult. For example, when separating variables in differential equations with power noniinearity, there is a need for the existing two arguments, to introduce three additional variables, resulting in the possibility of several options for solving this equation, which greatly complicates the analysis of the process.