Mathematical modelling plays an essential role in understanding numerous physical phenomena, often described by Differential Equations (DEs). However, handling these models, particularly when inundated with extensive data and inputs, poses challenges for both analytical and numerical approaches. Consequently, alternative techniques are sought. In this context, Artificial Neural Networks (ANNs) become valuable tool. Researchers have dedicated efforts to enhance ANNs capability in handling various types of DE’s such as Ordinary Differential Equations (ODE’s), Partial Differential Equations (PDE’s), and Nonlinear Partial Differential Equations (NPDE’s). This pursuit has led to advancements in learning algorithms tailored for ANNs. Currently, the Levenberg-Marquardt (LM) learning technique stands out as a popular method for training ANN models. Traditional learning techniques, marked by complexities such as the size of the Jacobian matrix, error stability, and computational intensity, have spurred the development of advanced learning techniques aimed at simplifying the training process. These advancements necessitate a thorough analysis of various ANN techniques, providing insights into selecting the most suitable approach for a given system. Consequently, the objective of this paper is systematically exploring the ANNs in solving mathematical models, shedding light on their application in diverse domains.