AP Calculus AB and BC glossary

Initial condition

An initial condition is a single known value of the solution, usually given as the output at a starting input. It is what pins down the constant of integration and turns a general solution into one particular curve.

Apply it as early as possible. Solving for the constant right after integrating is easier than carrying an unknown through the algebra and solving at the end.

The mistake

Forgetting the constant before applying the condition. Without a plus C in the general solution there is nothing left to solve for.

Appears in: Unit 7: Differential Equations