AP Calculus AB and BC glossary
Initial value problem
An initial value problem is a differential equation packaged with an initial condition. Solving it means finding the single solution curve that passes through the given point, rather than the whole family of curves the equation allows.
The standard route is separate, integrate both sides, apply the condition to find the constant, and only then solve for the dependent variable if the question asks for an explicit form.
The mistake
Solving for y before applying the condition. Doing the algebra first often buries the constant inside an exponential, where it is much harder to extract.
Appears in: Unit 7: Differential Equations