{"id":"differential-equation","domain":"analysis","type":"Concept","title":"Differential Equation","slug":"differential-equation","url":"/mathematics/analysis/differential-equation/","summary":"An equation relating a function to its derivatives. Primary mathematical language for physical laws describing rates of change. ODEs vs PDEs; linear vs nonlinear.","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Boyce, W.E. and DiPrima, R.C. (2012). Elementary Differential Equations. 10th ed."},{"tier":1,"citation":"Strogatz, S.H. (2015). Nonlinear Dynamics and Chaos. 2nd ed."},{"tier":2,"citation":"Fefferman, C.L. (2000). Existence and smoothness of the Navier-Stokes equation. Clay Mathematics Institute."},{"tier":3,"citation":"Gleick, J. (1987). Chaos: Making a New Science. Viking."}],"relationships":[{"type":"built_from","target":"derivative","label":"Derivative"},{"type":"related_to","target":"continuity","label":"Continuity"},{"type":"applied_in","target":"noethers-theorem","label":"Noether's Theorem — Lagrangian mechanics"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"2.1"}