Math 230 - Chapter 2 Study Guide

1. Given a direction field, sketch a solution curve that passes through the indicated point. Three parts.
2. Verify that the differential equation is exact and then solve it.
3. 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.
4. 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.
5. Find the integrating factor needed to make the equation exact. Do NOT solve the equation.
6. 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.
7. 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