# Math 230 - Chapter 2 Study Guide

1. Given the graph of the solution to a differential equation, determine which set of initial conditions was used. Multiple choice.
2. Given a direction field, sketch a solution curve that passes through the indicated point. Four parts.
3. Consider the autonomous differential equation. Identify the critical points, make a phase portrait, and identify whether each critical point is asymptotically stable, unstable, or sem-stable. Two parts.
4. Given a graph of several solution curves to an autonomous differential equation, identify the critical points, create a phase portrait, and classify each critical point as an attractor, repeller, or semi-stable. Finally, write an equation that could have the solutions shown.
5. Identify each differential equation as Autonomous, Separable, Linear, Exact, Homogeneous, Bernoulli, or None of these. More than one may apply and you should identify all that do apply. Nine parts.
6. Solve the differential equation using separation of variables.
7. Solve the differential equation using the integrating factor.
8. Verify that the differential equation is exact and then solve it.
9. Transform the differential equation into an exact differential equation and then solve.
10. Solve the differential equation by making an appropriate linear substitution.
11. Solve the homogeneous differential equation by making an appropriate substitution.
12. Solve the Bernoulli equation by making an appropriate substitution.

## Notes

• The first 5 problems need worked without a calculator or other technology. After you complete and turn in the first five problems, you get out your calculator and you may use Maxima to assist with the algebra and calculus for the remainder of the problems. However, you will still need to show the steps, it's just when you need to simplify, expand, integrate, differentiate, etc., you can use Maxima.
• You will need additional paper to complete the exam, there is not enough room on the test itself to complete the problems.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 Total 4 6 10 8 30 6 6 6 6 6 6 6 100