Differential Equation
Definition
An equation involving rates of change — the language physics uses to describe how things evolve.
Technical definition
An equation relating a function to its derivatives, e.g., m·d²x/dt² = −kx (harmonic oscillator) or dN/dt = −λN (radioactive decay). Solving gives the system's behavior over time; most of physics' fundamental laws are differential equations.
Example
Newton's second law F = ma is really m·d²x/dt² = F — a second-order differential equation whose solution is the object's entire trajectory.
Common confusion
Differential equations describe relationships, not answers — you must solve them (analytically or numerically) with initial conditions to get predictions. The equation alone does not tell you the motion.