# 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; circle all correct responses. Four parts.
2. Given a direction field, sketch a solution curve that passes through the indicated point. Three 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 semi-stable. Two 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. Eleven parts.
5. Find the integrating factor needed to make the equation exact and then multiply the equation by that. Do NOT solve the equation.
6. Use a linear substitution and then separate the variables. Do NOT solve the equation.
7. Use a substitution for a homogeneous differential equation and then separate. Do NOT solve the equation.
8. Convert the Bernoulli equation into a linear equation by making an appropriate substitution and then write in standard form. Do NOT solve the equation.
9. Solve the initial value problem using separation of variables.
10. Solve the initial value problem using the integrating factor.
11. Solve the exact differential equation.
12. 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

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 Total 4 6 6 33 6 6 6 6 8 8 8 6 103