CONDITIONAL LINEARIZABILITY OF FOURTH-ORDER SEMI-LINEAR ORDINARY DIFFERENTIAL EQUATIONS

Abstract

By the use of geometric methods for linearizing systems of second-order cubically semi-linear ordinary differential equations and the conditional linearizability of third-order quintically semi-linear ordinary differential equations, we extend to the fourth-order by differentiating the third-order conditionally linearizable equation. This yields criteria for conditional linearizability of a class of fourth-order semi-linear ordinary differential equations, which have not been discussed in the literature previously.

Keywords:

• Conditional linearization
• Lie linearization
• geometric method
• fourth-order ordinary differential equations