# Math 230 - Exam 1 Study Guide: Chapters 1-2

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. Two parts.
4. Given the general solution to a differential equation and the initial conditions, find the solution to the initial value problem.
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. Ten parts.
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. Besides the substitutions from section 2.4, this may also be to find the integrating factor needed to make the equation exact.
7. Solve the differential equation using either separation of variables or the integrating factor.
8. Identify the order of each differential equation and whether it is linear or non-linear. Four parts.

## Points Per Problem

 # Pts 1 2 3 4 5 6 7 8 All 6 10 10 6 40 10 10 8 100