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

翻译：微分方程是物理学、工程学、生物学和经济学中动态系统建模的基础工具。虽然解析解最为理想，但大多数实际问题仍需采用数值方法求解。本研究对三种主流计算软件——MATLAB、Mathematica和Maple——在求解各类微分方程（包括常微分方程（ODEs）、偏微分方程（PDEs）及微分方程组）方面进行了详细的对比分析。评估标准包括：语法与易用性（实现难度）、求解精度（与解析解对比）、计算效率（执行时间与资源占用）、可视化能力（图形输出的质量与灵活性）以及专业功能（针对特定问题类型的独特工具）。研究通过在三个平台上求解基准测试问题，系统讨论了三款软件各自的优势、局限性与适用场景。本文最后根据问题需求提出了选择最适用软件的具体建议。