A GROUP THEORETIC APPROACH TO A CLASS OF 2ND-ORDER ORDINARY DIFFERENTIAL-EQUATIONS NOT POSSESSING LIE POINT SYMMETRIES

We consider the solution of a class of second-order ordinary different ial equations not possessing Lie point symmetries by group theoretic m eans. The method involves increasing the order of these equations usin g homogeneity symmetry. The solution of this new third-order equation is then sought in the instances that it and the new reduced second-ord er equation possess additional symmetries. As a result the number of s econd-order equations solvable by the Lie theory of extended groups is increased.