On the equivalence of linear equations under nonlocal transformation

Linear nth order (n 3) ordinary differential equations have been shown to possess n + 1, n + 2 or n + 4 Lie point symmetries. Each class contains equations which are equivalent under point transformation. By taking the example of third order equations, we show that all linear equations are equivalent if the class of transformation is broadened to include nonlocal transformations and hence the representative of this class of equations is y(n) = 0.  2003 Elsevier Inc. All rights reserved.