# Math 230 - Chapter 4 Study Guide

1. 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.
2. Use reduction of order to find a second solution. Look at problems 4.2.1-16.
3. Find the general solution of the differential equation with constant coefficients. Two parts. Look at problems 4.3.1-28.
4. Solve the boundary-value problem. Look at problems 4.3.37-40.
5. Find a linear differential operator that annihilates the given function. Two parts. Look at problems 4.5.15-26.
6. Solve the differential equation by undetermined coefficients using the superposition method. Look at problems 4.4.1-26.
7. 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 yp, but you should identify which parts of the general solution are yc and which are yp. Look at problems 4.5.35-64.
8. Solve the differential equation using variation of parameters. Look at problems 4.6.1-18.
9. Solve the Cauchy-Euler differential equation. Look at problems 4.7.1-18.
10. Solve the system of differential equations by systematic elimination. Look at problems 4.8.1-20.
11. 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

 # Pts 1 2 3 4 5 6 7 8 9 10 11 Total 7 8 14 9 8 9 9 9 9 9 9 100