Said Waqas Shah, F. M. Mahomed, H. Azad, and M. T. Mustafa. Complete Classification of Scalar Fourth-Order Ordinary Differential Equations and Linearizing Algorithms. Dynamic Systems and Applications 30 (2021) No.3, 519-534  

https://doi.org/10.46719/dsa202130313

ABSTRACT.
A complete classification of fourth-order ODEs according to the symmetry algebras they admit is carried out. Applications to linearization and physical models in fluids and beam theory are also presented.

AMS (MOS) Subject Classification. 34C14, 34C20

Key Words and Phrases. Ordinary differential equations, Symmetry, Applications to beam theory and fluid motion.