# Math 230 - Chapter 4 Study Guide

1. The roots of the auxiliary equation are given. Write the complementary solution and the form of the particular solution. (3 parts)
2. Write an operator that will annihilate each expression. (4 parts)
3. Write the general solution to the differential equation. (3 parts)
4. Find the largest interval containing a point where the functions are linearly independent.
5. Given one solution to a homogeneous differential equation, use reduction of order to find a second solution.
6. Rewrite the Cauchy-Euler equation with constant coefficients and as a function of t. Do not solve.
7. Solve the Cauchy-Euler differential equation.
8. Use the substitution to solve the equation.
9. Solve the system of differential equations.
10. Solve the non-homogeneous differential equation. (4 parts)
11. The general solution to an equation is given, use variation of parameters to find the particular solution.
12. The general solution to a second order homogeneous linear differential equation is given. Identify whether the given conditions form an initial value problem or boundary value problem. Find the constants that satisfy the given conditions. (3 parts)

## Notes

• Examples of each type of problem can be found in the wiki.
• You will need to bring scratch paper for extra work.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 Total 12 8 6 5 7 5 7 7 7 20 7 9 100