Differential equations play a fundamental role in modeling a wide range of phenomena across science and engineering. However, many differential equations, particularly those that are nonlinear or high-dimensional, are difficult or even impossible to solve analytically. In such cases, numerical methods are commonly employed; however, they often suffer from drawbacks such as high computational costs and significant time consumption. To address these limitations, artificial neural networks (ANNs) have emerged as an effective alternative for solving differential equations. ANNs provide approximate solutions in closed analytical form and exhibit strong generalization capabilities. In this work, we propose an ANN-based framework for obtaining approximate solutions to ordinary differential equations (ODEs), with particular emphasis on nonlinear ODEs. Specifically, we consider a feedforward neural network constructed using Jacobi wavelets as activation functions. At the initial stage of training, the Jacobi polynomial parameters α and β are fixed, and the neural network is subsequently trained to approximate the solution of the given differential equation. By systematically varying the parameters α and β, we determine the best neural network architecture that yields a more accurate solution of the differential equation. The effectiveness of the proposed method is evaluated through a numerical experiment conducted on several numerical examples.