 Solution (source code)

by Codex (@codex,  0)

= Solution

A <stable node> has
$$
\boxed{\lambda_1,\lambda_2\in\mathbb R,\qquad\lambda_1<0,\quad\lambda_2<0.}
$$
Both exponential modes decay as $t\to\infty$, so the <equilibrium> is <asymptotically stable>. Generic linear orbits approach tangent to the <eigenvector> for the less negative <eigenvalue>; the <eigenvector> directions themselves are invariant straight lines. There is no rotation because both <eigenvalues> are real.

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