differential-equations-solver

The differential-equations-solver skill is designed to provide expert-level guidance on ordinary differential equations (ODEs) and partial differential equations (PDEs). It focuses on solution methods, qualitative analysis, and applications relevant to physics and engineering. The skill is intended to support structured problem solving and theoretical understanding in mathematical modeling contexts. However, it is currently marked as a legacy template and requires updated research validation before being relied upon for high-confidence results.

The skill includes a defined research-driven workflow to ensure accuracy and freshness. Users are instructed to begin with a research checklist, review known gaps, and load topic-specific modules only after verification. Core guidance is preserved for review, while validation tasks and open questions are explicitly documented. The documentation emphasizes capturing up-to-date sources, maintaining a source log, and upgrading confidence levels only after proper validation. This structured approach ensures that any applied guidance is systematically reviewed and improved over time.

Typical use cases include academic study, theoretical review, and engineering-related analysis involving differential equations. Target users include students, researchers, educators, and engineers who require structured methodological support for ODE and PDE analysis. Because the skill currently has low confidence status and pending research updates, it is best suited for controlled review workflows rather than production-critical or high-stakes applications until its validation status is upgraded.