# Math 230 - Chapter 2 Study Guide

- Given a direction field, sketch a solution curve that passes through the
indicated point. Three parts.
- Verify that the differential equation is exact and then solve it.
- Consider the given autonomous differential equation. Identify the critical points, make a phase portrait, and identify whether each critical point is asymptotically stable, unstable, or
semi-stable. Three parts.
- 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. Ten parts.
- Find the integrating factor needed to make the equation exact. Do NOT solve the equation.
- Use one of the substitutions (homogeneous, Bernoulli, or linear) from section 2.5 and manipulate it into the desired format (separated or linear). Do NOT solve the equation.
- Solve the differential equation using either separation of variables or the integrating factor.

## Notes

- You will need additional paper to complete the exam, there is not enough room on the test itself to complete the problems.
- There are 103 points possible, but the exam is only worth 100 points in the gradebook.

## Points per problem

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
Total |

Pts |
6 |
10 |
21 |
40 |
8 |
8 |
10 |
103 |