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Third-order ordinary differential equations Y”’ = f(x, y, y’’, y′”) with maximal symmetry group

Ahmad Y. Al-Dweik


We present here, in compact form, the necessary and sufficient conditions for linearization of third-order ordinary differential equations y ′′′ = f(x; y; y ′ ; y ′′ ) with  maximal symmetry group via point transformation. A simple procedure to construct the point transformation using the isomorphism of the symmetry sub-algebra sl(2;R) is also presented. This subalgebra is the semi-simple part of the Levi-Decomposition for the 7-dimensional symmetry algebra.

Mathematics Subject Classication (2010): 34A05, 34A25, 53A55, 76M60.

Key words: Linearization, third order ODEs, point transformation, contact transformation, Lie symmetries, relative differential invariants.