  Using geometric methods for linearizing systems of second order cubically
semi-linear ordinary differential equations and third order quintically
semi-linear ordinary differential equations, we extend to the fourth order by
differentiating the third order equation. This yields criteria for
linearizability of a class of fourth order semi-linear ordinary differential
equations, which have not been discussed in the literature previously. It is
shown that the procedure can be extended to higher order. Though the results
for the higher orders are complicated, they are doable by algebraic computing.
The standard Lie approach, as developed at present does not seem to be amenable
to giving results that can be handled even by algebraic computing.
