Symbolic implementation of preliminary group classiffication for ordinary differential equations (Q1791420)

Summary: We apply the method of preliminary group classification to ordinary differential equations of the form \(y^{(n)}=E(x,y,y^\prime,\ldots,y^{(n-1)}\), \(f^i(x))\), \(i=1,\ldots,m\). We show how this method can be implemented via the popular symmetry analysis package PROGRAM LIE provided that the package is supplemented with a small file. We then apply this method to an extension of the generalised Emden-Fowler equation given by \(y^{\prime\prime} =\sum_{i=2}^5 f^i(x)y^i\).