Dai Jiayuan , pp. 27. ING/School of Engineering, 2012.
Based on symmetry and invariance principles, Lie group analysis is the only systematic method for solving nonlinear differential equations analytically. Nonlinear second-order ordinary differential equations admitting two-dimensional Lie algebras can be transformed into one of the four types of canonical forms via Lie's integration method. In this thesis, Lie's second-order equation of type III is considered from the point of view of equivalence transformations. The generators of the equivalence group and the principal Lie algebra are calculated.