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

Points per problem

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