# Math 230 - Final Exam Study Guide

1. Use separation of variables to solve the differential equation.
2. Use the integrating factor to solve the differential equation.
3. Verify that the differential equation is exact and then solve it.
4. Find the general solution to the differential equation with constant coefficients.
5. Solve the Bernoulli differential equation.
6. Use the superposition approach to the method of undetermined coefficients to solve the differential equation.
7. Use the annihilator approach to the method of undetermined coefficients to solve the differential equation.
8. Solve the Cauchy-Euler differential equation.
9. Use variation of parameters to solve the differential equation.
10. Use the Laplace transform to solve the differential equation.
11. Use the Laplace transform to solve the integrodifferential equation.
12. Use eigenvalues and eigenvectors to solve the system of linear differential equations. Find the eigenvalues by hand, but then use Derive to find the eigenvectors. Show Derive's output and the eigenvector you created from that. Finally, write the solution to the system.
13. Use variation of parameters to solve the system of linear differential equations.
14. Form a power series solution to a differential equation. Make the subsitutions into the differential equation and simplify until there is a single summation. Then write the recurrence relation. Do NOT find terms or solve the differential equation completely.
15. A differential equation is written using its series solution format. Find the indicial roots and write the recurrence relations for each indicial root. Find the two linearly indifferential equationpendifferential equationnt solutions to the differential equation.

## Notes

• This test is open notebook.
• Your notebook may contain notes, homework, tests, notation, and tables.
• It may not include the textbook or photocopies out of the textbook with the exception of the table of integrals from the front cover and the table of Laplace transforms from the back cover.
• You should use Derive where appropriate to find things like partial fraction expansions, products and inverses of matrices. Copy the important results from Derive onto the test as your work.
• You do not need to answer the test questions in the order presented. Go through and answer the ones you know how to do without looking at your notes first.
• If a problem gives you difficulty, move on and come back to it later.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total 12 12 12 12 12 14 14 14 14 14 14 14 14 14 14 200