Differential equations

Equations where the unknown is a function — and a derivative is in there too.

A differential equation relates a function to its derivatives. Solutions are *functions*, not numbers. They model populations, cooling, motion, electric circuits — anything that changes.

Try it

dy/dx = y

Functions whose derivative is themselves. Answer: y = Ce^x. Try it: d/dx(Ce^x) = Ce^x. ✓

Why they matter

Newton's second law (F = ma = m · d²x/dt²) is a differential equation. Almost every physical law is one.