a. (4 points.) Given Van der Pol equation: y" - μ(1 − y²)y' + y = 0. Determine the type of the critical point at (0, 0) when μ > 0, μ = 0, μ<0. b. (4 points.) Rayleigh equation. Show that the Rayleigh equation Y" − μ (1 − −³½³½³¹²) Y² + Y = 0 (μ> 0) also describes self-sustained oscillations and that by differentiating it and setting y = Y' one obtains the van der Pol equation. c. (4 points.) Duffing equation. The Duffing equation is y" + wy+By³ = 0 where usually ẞ is small, thus characterizing a small deviation of the restoring force from linearity. ẞ> 0 and ẞ< 0 are called the cases of a hard spring and a soft spring, respectively. Find the equation of the trajectories in the phase plane. (Note that for ẞ> 0 all these curves are closed.)