AP Calculus BC glossary

Equilibrium solution

An equilibrium solution is a constant function that satisfies a differential equation, found by setting the derivative expression to zero and solving. On a slope field it shows up as a horizontal line that other solution curves approach or run away from.

For the logistic equation the equilibria are $P = 0$ and $P = L$ . The carrying capacity is stable, since nearby solutions move toward it, while zero is unstable.

The mistake

Losing equilibrium solutions during separation of variables. Dividing by the very factor that is zero removes those solutions from the answer.

Appears in: Unit 7: Differential Equations