Differential Equation
A mathematical equation relating an unknown function to its derivatives with respect to one or more independent variables.
Governing formula
F(x, y, y', y'', ..., y^(n)) = 0, d²y/dx² + ω² y = 0
SI unit
Mathematical Equation Class
In depth
Differential equations govern continuous change across almost all subfields of physics. Ordinary Differential Equations (ODEs) involve functions of a single variable (like time in classical mechanics), while Partial Differential Equations (PDEs) involve multiple independent variables (like space and time in Maxwell's equations or the Schrödinger equation).
Examples in the real world
Newton's second law F = m d²x/dt² forming a second-order ODE for particle trajectories, and heat conduction PDEs.