Suggest the damped harmonic oscillator, given by
x'' + 2x'+ 9 x = 0 . Rewrite as a system of two first order ODEs
Find all fixed points of the system
Give the eigenvalues of the coefficient matrix
For each eigenvalue, give an eigenvector
Use the eigenvalues to characterize the fixed point
Use Euler's formula to write the general solution in terms of damped oscillations.