Any real physical problem arising in fluid mechanics, when it is translated to mathematical approach generally govern a differential equation with some assumptions. The solution for such a study of the system is solved using analytical or numerical techniques. An attempt has been made to understand the characteristics or behavior or analysis of the physical system using different methods like Lighthills method, perturbation methods, rational approximation or Pad approximation, shooting technique and also highlights on the advantages and limitations of each method are discussed.