The system <matrix> has <eigenvalues> $2$ and $3$, with <eigenvectors> in the directions $y=-x$ and $y=-x/2$, respectively. Both <eigenvalues> are positive, so the origin is an unstable node. The two eigendirections are straight trajectories directed away from the origin. Every other trajectory also moves outward, tangent near the origin in backward time to the faster eigendirection and asymptotic in forward time to the eigenvalue-$3$ direction.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ia / Paper 2 / 8A / a / Solution

 Solution (source code)