In the paper, constructive methods for finding some first integrals of a sixth-order ordinary differential equation with a potential operator are suggested. We use some methods based on application of transformation of variables to establish invariance of the given sixth-order ordinary differential equation with the potential operator and the corresponding Hamilton-Ostrogradskii action. Some first integrals of the considered equation are also found.
Huyen Luu (Fri,) studied this question.