AP Calculus AB and BC glossary

Particular solution

Also called: Initial value problem

A particular solution is the one member of a differential equation's solution family that passes through a specified point. The initial condition is what determines the arbitrary constant and selects that single curve.

The order matters. Find the general solution first, substitute the initial condition to solve for the constant, then write the final answer with that value in place.

Substitute early when separating

In a separable equation it is often cleaner to apply the initial condition right after integrating, before rearranging, because the constant is easier to isolate at that stage.

Appears in: Unit 7: Differential Equations