Symmetries and exact solutions of a multiplicative class of differential equations with exponential functions

This article studies discrete symmetries of a class of 2nd order ordinary differential equations with multiplicative right values.Discrete transformations closed in the studied class of equations are found. The discrete group of transformations and its graph are constructed. All elements of the orbit of the original multiplicative equation containing the exponential function are obtained. The method of finding exact solutions of the equations of the specified orbit at some values of the parameters included in the equations is presented. Examples of finding solutions to the equations of this orbit are discussed.In this work, the method of extending the class of equations, as well as the method of "multiplication" of solvable cases in the studied class of equations, based on the fact that solutions of equations are related by the same transformations as the equations themselves, are used.