Kubayi, Jollet Truth2023-11-132023-11-132022https://hdl.handle.net/10539/36963A dissertation submitted in fulfilment of the requirements for the degree of Master of Science to the Faculty of Science, University of the Witwatersrand, Johannesburg, 2022This dissertation will be divided into two parts. The first part will involve the use of symmetries to find exact solutions of higher order difference equations. The second part will deal with important ordinary differential equations, in the search for singularities and integrability testing. We will analyse a Painlev´e equation, Ivey’s equation, the higher-order Lane-Emden type equation and a class of third-order boundary flow equations.enARS AlgorithmInvariance AnalysisOrdinary Difference EquationsDissertation