Can LLMs Solve Ordinary Differential Equations? A Comparative Analysis - Samanjata, Domingos; Santin, René Vieira; Marcacini, Ricardo Marcondes; Rezende, Solange Oliveira (Anais do Simpósio Brasileiro de Banco de Dados (SBBD); 2026: Anais do XLI Simpósio Brasileiro de Bancos de DadosDO - 10.5753/sbbd.2026.249229, 2026)
Solving Ordinary Differential Equations (ODEs) requires mathematical modeling and reasoning skills that remain challenging for large language models (LLMs). This paper evaluates five LLMs, DeepSeek-R1, Claude-Haiku-4.5, Llama-3.3-70B-Instruct, Gemini-2.5-Pro, and GPT-5.2, using ten first-order ODE application problems and a task involving analogous problem generation. We propose a multi-dimensional framework assessing mathematical modeling, Python code generation, solution accuracy, and the generation of analogous problems. Results show strong modeling performance across all models (96%–98%), demonstrating their ability to translate natural language descriptions into mathematical formulations; when generating analogous problems, scores ranged from 85% to 100%, enabling direct performance comparisons against each model’s own baseline. However, performance declines in code generation tasks, exposing limitations in multi-step reasoning and execution. Claude-Haiku-4.5 achieves the highest overall score (84%), while Llama-3.3-70B-Instruct performs best in code generation. GPT-5.2 records the lowest overall performance. These findings reveal a gap between conceptual understanding and reliable end-to-end problem solving, highlighting the importance of human oversight and hybrid symbolic-numerical approaches.