Nonlinear Systems & Linearization · Challenge problem

The van der Pol oscillator $x'' + \mu(x^2 - 1)x' + x = 0$ with $\mu > 0$ has an unstable equilibrium at the origin of the phase plane $(x, y) = (x, x')$. For small $\mu$ it is an unstable spiral. Find the smallest $\mu$ at which it becomes a node (the eigenvalues of the linearization become real).