Reading through my notes in dynamical systems. I get to a point where it asks to write the Van der Poll equation as the state space form.
$\ddot \theta - \mu (1 - \theta^2) \dot \theta + \theta = 0$
$x_1 = \theta$ and $x_2 = \dot x_1$
$\dot x_1 = x_2$
$\dot x_2 = -x_1 - \mu x_2 x_1^2 + \mu x_2$
But because of the second term of $\dot x_2$ I don't know how to put it in state space form since it is a non-linear term. Any advise on how to do it? Is there a way to linearize this system?