# 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; circle all correct responses. Four parts.
- Given a direction field, sketch a solution curve that passes through the
indicated point. Three 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
semi-stable. Two 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. Eleven parts.
- Find the integrating factor needed to make the equation exact and then
multiply the equation by that. Do NOT solve the equation.
- Use a linear substitution and then separate the variables. Do NOT solve the equation.
- Use a substitution for a homogeneous differential equation and then separate. Do NOT solve the equation.
- Convert the Bernoulli equation into a linear equation by making an appropriate substitution and then write in standard form. Do NOT solve the equation.
- Solve the initial value problem using separation of variables.
- Solve the initial value problem using the integrating factor.
- Solve the exact differential equation.
- Use Euler's method to approximate a value.

## Notes

- The first 4 problems need worked without a calculator or other technology. You do not need to show work on this part of the exam, although you may if you wish.
- After you complete and turn in the first 4 problems, you will be given the second part. You may use your calculator, but not Maxima, Winplot, or other technology on this part of the exam.
- You should show work on all problems on the second part.
- You will need additional paper to complete the exam, there is not enough room on the test itself to complete the problems.
- When working through the first part, do not forget there is a second part. In other words, watch your time and move quickly throught the first page. Consider the points when you think about how much time you're going to spend on a problem.
- There are 103 possible points on the exam, but it is only worth 100 points.

## Points per problem

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

Pts |
4 |
6 |
6 |
33 |
6 |
6 |
6 |
6 |
8 |
8 |
8 |
6 |
103 |