Conditional linearizability of higher order ordinary differential equations

Abstract:
Lie provided criteria for scalar, second order ordinary differential equations (ODEs) to be convertible to linear form by point transformations. This was extended by Neut and Petitot and by Ibragimov and Meleshko to the third order and by Ibragimov and Meleshko to the fourth order. Geometrical methods were used by Mahomed and Qadir to provide criteria and methods to convert systems of second order ODEs to linear form. In all these cases the number of linearly independent solutions is equal to the order of the ODEs. Mahomed and Qadir also developed a procedure to obtain solutions of third order ODEs and systems of ODEs that may have only two linearly independent solutions. This was called conditional linearizability. Here this procedure is extended to higher orders.