Differential Equations

Quick Notes

For these problems, you will be given a differential equation, often in context. The problems appear almost every year on the FRQ of both exams.
This will most likely be a non-calculator question.
Most of the time, you will be asked to solve the differential equation using separation of variables. Remember that the solution to a differential equation is an equation.
You may be asked to find the general solution (don't forget the + C) or the particular solution using initial condition.
Every part of the solving process is generally worth a point, so show every step!
The problems often include exponential growth or decay. The differential equation could be described verbally using proportionality.
These questions may involve some analysis of the function as well.
Regarding slope fields on the FRQ, you should be prepared to sketch and interpret a slope field for a differential equation as well as sketch a particular solution going through a given point using the slope field.
Regarding slope fields on the MCQ, you may be asked to match a slope field to its differential equation, one way or the other.
On the BC exam, Euler's Method is very common.
On the BC exam, you may see Logistic models in addition to exponential growth or decay.