Math 230 - Chapter 4 Study Guide

  1. The roots of the auxiliary equation are given as well as the right hand side of the non-homogeneous equation. Write the complementary solution and the form of the particular solution. (3 parts)
  2. Write an operator that will annihilate each expression. (3 parts)
  3. Given the equation using the D notation (example: D(D+1)y=0), write the general solution to the differential equation. (3 parts)
  4. Use the method of undetermined coefficients to find the particular solution. The form of the particular solution is given along with the simplification from Maxima when the particular solutions is plugged into the differential equation. (2 parts).
  5. Find the largest interval containing a point where the functions are linearly independent.
  6. Solve the homogeneous differential equation. This may be constant coefficients or Cauchy-Euler. (7 parts)
  7. A differential equation is given in annihilator format as well as the values of u1', u2', and u3' are given. Write the complementary solution and use variation of parameters to find the particular solution.
  8. Solve the system of linear differential equations. Combine parameters from x(t) and y(t) so that only c1 and c2 are used.
  9. The Wronskian and associated determinants for L(y)=g(x) are given. Use them to find the complementary solution, g(x), the annihilator for the corresponding homogeneous differential equation, the annihilator for the non-homogeneous differential equation and the functions u1', u2', and u3'. In addition, write the original equation in Lagrange's notation (y, y', y'', ...). You do not need to actually find for the particular solution.


Points per problem

# 1 2 3 4 5 6 7 8 9 Total
Pts 12 9 9 6 5 35 6 6 12 100