DISCRETE GROUPS AND SOLUTIONS OF POWER DIFFERENTIAL EQUATIONS OF THE ORBIT OF TANGENTS OF THE GENERALIZED EMDEN-FOWLER EQUATION

Khakimova Zilya Nailevna

We consider a class of ordinary differential equations of the 2nd order with power right-hand sides, a subclass of which is the generalized Emden-Fowler equation (GEFE). For one equation from the GEFE class, the general solution of which is related to the trigonometric and hyperbolic cosine and tangent functions, a discrete 78th order transformation group is constructed, subgroups of which are the 6th and 12th order dihedral transformation groups, also the graphs of these discrete groups are constructed. All equations of the orbit of the original equation from the GEFE class are found and general solutions of these equations are calculated.

Keywords:generalized Emden-Fowler equation (GEFE), 2nd order ordinary differential equation, differential equation with power right side, discrete transformation group, dihedral group, exact solution of the differential equation