1. The problem statement, all variables and given/known data Examine the equation x¨ + β(x^2 − 1)x˙ + x = 0 Explain qualitatively the motion in three cases: |x| < 1, |x| > 1, and |x| = 1. In each case, do you expect the motion to be bounded our unbounded? Define the energy of the system as E ≡ 1/2 (x^2 + v^2). Show that the time rate of change of the energy is β(1 − x^2)v^2 Examine for each of the three cases in which case is energy a conserved quantity? What happens in the other cases? 2. Relevant equations x¨ + β(x^2 − 1)x˙ + x = 0 3. The attempt at a solution I have no idea how to go about this question, the differential equation is not solvable. How do you examine it then?