## Group classification of the generalized Emden-Fowler-type equation.(English)Zbl 1191.34045

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.

### MSC:

 34C14 Symmetries, invariants of ordinary differential equations 34A26 Geometric methods in ordinary differential equations 34A05 Explicit solutions, first integrals of ordinary differential equations
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### References:

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