# Math 230 - Exam 1 Study Guide

- Identify the order of each differential equation and whether it is linear or non-linear. Four parts.
- Find the values of
*m* so that the function y = e^{mx} is a solution.
- Find the values of
*m* so that the function y = x^{m} is a solution.
- Verify the one parameter family of curves is a solution.
- Verify the pair of functions is a solution to the system of linear equations..
- Given a differential equation and its general solution, find the solution to the initial value problem.
- Given a differential equation and its general solution, find the solution to the initial value problem.
- Determine a region in the xy-plane that has a unique solution.
- Application problem - spread of flu
- Application problem - mixture
- Application problem - drug in bloodstream
- Application problem - memorization

## Notes

- This is a take home exam.
- For the questions that ask you to verify a solution, you may use Maxima to help find derivatives, but you should show work as far as the substitution into the equation.
- There is a bonus question #13 worth up to 5 additional points. Use winplot to graph the differential equations for the application problems and estimate when something happens. You might want to go into the Table of Contents in the wiki and choose Winplot. Then look at the "Numerical Solver" section of "A Numerical Method" and/or the "Direction Fields, Winplot" pages. You will probably have to change your viewing window in Winplot.

## Points per problem

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

Pts |
5 |
4 |
4 |
4 |
4 |
4 |
4 |
2 |
5 |
5 |
5 |
5 |
50 |