# 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

• You may use wxMaxima for the last two problems on the test as they involve partial fractions or integration by parts.
• You may not use the computer on the rest of the test, so you'll need to turn it in before you start using wxMaxima.
• You should show work on the test, but bring extra paper to use in case there isn't enough room on the test itself.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 Total 4 8 12 7 27 7 7 7 7 7 7 7 100