Analyzing Computational Approaches for Differential Equations: A Study of MATLAB, Mathematica, and Maple

Differential equations are fundamental to modeling dynamic systems in physics, engineering, biology, and economics. While analytical solutions are ideal, most real-world problems necessitate numerical approaches. This study conducts a detailed comparative analysis of three leading computational software packages: MATLAB, Mathematica, and Maple in solving various differential equations, including ordinary differential equations (ODEs), partial differential equations (PDEs), and systems of differential equations. The evaluation criteria include: Syntax and Usability (ease of implementation), Solution Accuracy (compared to analytical solutions), Computational Efficiency (execution time and resource usage), Visualization Capabilities (quality and flexibility of graphical outputs), Specialized Features (unique tools for specific problem types). Benchmark problems are solved across all three platforms, followed by a discussion on their respective strengths, weaknesses, and ideal use cases. The paper concludes with recommendations for selecting the most suitable software based on problem requirements