# Math 230 - Chapter 4 Study Guide

- Use the Wronskian to determine whether the given set of functions is linearly
independent on the specified interval. Look at problems 4.1.15-22.
- Use reduction of order to find a second solution. Look at problems 4.2.1-16.
- Find the general solution of the differential equation with constant coefficients.
Two parts. Look at problems 4.3.1-28.
- Solve the boundary-value problem. Look at problems 4.3.37-40.
- Find a linear differential operator that annihilates the given function.
Two parts. Look at problems 4.5.15-26.
- Solve the differential equation by undetermined coefficients using the
superposition method. Look at problems 4.4.1-26.
- Find the general solution to the differential equation using the annihilator
approach. You do not need to use undetermined coefficients to find the constants
in y
_{p}, but you should identify which parts of the general solution
are y_{c} and which are y_{p}. Look at problems 4.5.35-64.
- Solve the differential equation using variation of parameters. Look at
problems 4.6.1-18.
- Solve the Cauchy-Euler differential equation. Look at problems 4.7.1-18.
- Solve the system of differential equations by systematic elimination. Look
at problems 4.8.1-20.
- Solve the differential equation using the substitution u = y'. Look at
problems 4.9.3-8.

## Notes:

You may have a note card with certain formulas on it. These cards may not
have worked out examples. Here are the formulas you may have:

- From section 4.2, you may have formula 5 for reduction of order.
- From section
4.5, you may have a list of the different annihilators and what they annihiliate.
- From
section 4.6, you may have formulas 3 and 5.

## Points per problem

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

Pts |
7 |
8 |
14 |
9 |
8 |
9 |
9 |
9 |
9 |
9 |
9 |
100 |