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

A particular solution must satisfy the differential equation and pass through the given point, so both conditions are worth checking before you move on. Substituting the initial point back into your final expression catches most sign and constant errors.

Appears in: Unit 7: Differential Equations