Quasi-Lie schemes and Emden–Fowler equations.

The recently developed theory of quasi-Lie schemes is studied and applied to investigate several equations of Emden type and a scheme to deal with them and some of their generalizations is given. As a first result we obtain t-dependent constants of the motion for particular instances of Emden equations by means of some of their particular solutions. Previously known results are recovered from this new perspective. Some t-dependent constants of the motion for equations of Emden type satisfying certain conditions are recovered. Finally new exact particular solutions are given for certain cases of Emden equations. [ABSTRACT FROM AUTHOR]