Take the Van Der Pol equation $x'' - 3(1-x^2)x' + x = 0$.

Write down the corresponding first order system using the extra variable $y$:
$x' = {}$
$y' = {}$

Compute the Jacobian matrix for all $x$ and $y$: $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$

There is a critical point at the origin. The behavior is
For behavior write one of "saddle", "source", "sink", "spiral sink", "spiral source", "center".