A differential equation relates a function to its derivatives. Instead of solving for a number, you solve for a function. The equation dy/dx = 2x, for example, has the solution y = x² + C, where C is any constant.

These equations model change. Newton's second law, F = ma, is a differential equation. So are the heat equation, the wave equation, and the equations of fluid flow. Population growth, radioactive decay, and electrical circuits all lead to differential equations.

Solving them can be done analytically for simple cases, but most require numerical methods. Computers approximate solutions by stepping through time or space in small increments. The field divides into ordinary differential equations (one variable) and partial differential equations (several variables). Both are central to physics, engineering, and applied mathematics.

• Equation involving derivatives
• Solution is a function, not a number
• Models change in physics and engineering
• Often solved numerically