Solve the following system of differential equations given that and has eigenvalues and with eigenvectors and respectively.
1) The system can be rewritten as a matrix:
2) The system will have the same number of solutions as eigenvalues and each solution will have the form . Therefore, this system has two solutions that by the superposition principle can be added together.
  3) The C constants are determined by solving for the given initial conditions and .
  This amounts to solving the following system:
  After row reduction we obtain:
  So the final solution is the following: