Group classification of the generalized Emden-Fowler-type equation
This work is devoted to the [group-theoretical] analysis of the generalized Emden-Fowler equation \[ xu^{\prime\prime}+nu^{\prime}+x^{\nu}F(u)=0. \] In dependence of the function \(F(u)\), the point symmetries of the equation are found, which gives eight possible cases. Up to the well known linearizable case, the number of these symmetries does not exceed three. These are then compared with the Noether symmetries in order to obtain first integrals. The symmetries are applied in some cases to reduce the corresponding equation.
scientific article; zbMATH DE number 5632767
scientific article