The subject of these lectures will be the study of the advantages that can be derived when integrating differential equations of motion from a special form of these equations. In Analytical Mechanics, you can find everything related to the problem of compiling and transforming differential equations, but very little has been done to integrate them. The mentioned task is barely set; the only thing that can be attributed to this is the constant variation method - the approximation method, which rests on a special form of differential equations found in mechanics.