On the equivalence of linear equations under nonlocal transformation. (Q1417973)

Scalar linear third-order ordinary differential equations are studied via nonlocal transformations. Nonlocal transformations of such equations to the simplest third-order equation are obtained. `Equivalence' is used without stating clearly what is meant by it. The authors refer to their preprint appeared in 1995 for contact symmetries instead to a more general work, e.g., of \textit{C. Wafo Soh}, \textit{F. M. Mahomed} and \textit{C. Qu} [Nonlinear Dyn. 28, No. 2, 213--230 (2002; Zbl 1015.34026)]. Also the discussion on \(n\)th-order equations is incomplete. The statement: `This will result in an (n-1)th-order linear equation which is equivalent to \(y^{(n-1)}=0\) under a point transformation' is not true.