What are Differential Equations?

Differential equations describe how quantities change over time or space. They're essential for modeling real-world phenomena in physics, engineering, biology, economics, and more.

What is a Differential Equation?

A differential equation relates a function to its derivatives. For example, dy/dx = 2x describes how y changes with respect to x. The solution is y = x² + C.

First-Order Equations

First-order equations involve only the first derivative. They model exponential growth/decay, cooling, and simple motion. Solutions often involve exponential functions.

Second-Order Equations

Second-order equations involve the second derivative. They model oscillations, springs, circuits, and waves. Solutions often involve sine and cosine functions.

Real-World Applications

Differential equations model population growth, heat transfer, fluid dynamics, electrical circuits, quantum mechanics, and economic systems. They're the language of change.