Past exam of the algebra, analysis and differential equations II course of the University of Oxford / 2008 printed variant / 9 / a / i

Both eigenvalues are real and negative: $\boxed{{\lambda }_1<0,{\lambda }_2<0}$, with distinctness as assumed. The two independent real eigendirections carry exponentially decaying factors $e^{{\lambda }_{j}t}$, giving a stable node.