AP Calculus AB and BC glossary

General solution

The general solution of a differential equation is the entire family of functions that satisfy it, expressed with an arbitrary constant. Every specific solution is obtained by choosing a value for that constant.

Because the constant is unspecified, the general solution describes infinitely many curves at once, which is precisely what a slope field draws. Any one of them is a particular solution.

Solve for y

An answer left in implicit form is usually incomplete on the AP exam. Unless the question says otherwise, isolate yy before finishing.

Appears in: Unit 7: Differential Equations