AP Calculus AB and BC glossary

Differential equation

A differential equation is an equation that relates an unknown function to its own derivatives. Its solution is a function rather than a number, and there is usually a whole family of them until an initial condition picks one out.

The equation $\frac{dy}{dx} = 2x$ asks which function has derivative $2x$ , and the answer is the family $y = x^2 + C$ . Verifying a proposed solution is a matter of differentiating it and checking the equation holds.

AP Calculus covers separable equations, which are the ones you can rearrange so each variable sits with its own differential, plus slope fields and Euler's method for the ones you cannot solve exactly.

Appears in: Unit 7: Differential Equations