# Math 230 - Chapter 2 Study Guide

- Given the graph of the solution to a differential equation, determine which
set of initial conditions was used. Multiple
choice.
- Given a direction field, sketch a solution curve that passes through the
indicated point. Four parts.
- 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.
- 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.
- 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.
- Solve the differential equation using separation of variables.
- Solve the differential equation using the integrating factor.
- Verify that the differential equation is exact and then solve it.
- Transform the differential equation into an exact differential equation and then solve.
- Solve the differential equation by making an appropriate linear substitution.
- Solve the homogeneous differential equation by making an appropriate substitution.
- 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

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
Total |

Pts |
4 |
8 |
12 |
7 |
27 |
7 |
7 |
7 |
7 |
7 |
7 |
7 |
100 |