Computer construction of the general solution of the special form of the Abel differential equation

Abstract

The computer method of building a general solution of the special form for the nonlinear differential equation of the second order and the Abel differential equation of the first kind is considered. Three examples which contain the solutions of the initial problem are presented. The module allowing to visualize partial solutions of the Abel differential equation for the given values of parameters has been built. For the obtained solutions the visualization in the real numbers domain is represented. All the calculations and visualizations are realized in the Mathematica 10 system.