Conditional Linearizability Criteria for Third Order Ordinary Differential Equations

Abstract

Using geometric methods for linearizing systems of second order cubically non-linear in the first derivatives ordinary differential equations, we extend to the third order by differentiating the second order equation. This yields criteria for conditional linearizability via point transformation with respect to a second order equation of classes of third order ordinary differential equations, which are distinct from the classes available in the literature. Some examples are given and discussed.