 Solution

ID: past-exam-of-the-algebra-analysis-and-differential-equations-2-course-of-the-university-of-oxford/2012/7/a/v/solution

λ_{1, 2} = α \pm i β, α < 0, β \neq = 0.

In suitable real coordinates the radius decays like

e^{α t}

while the angle changes at rate

β

. The orbit therefore spirals towards the equilibrium, which is asymptotically stable. This is also called a stable focus.

 New to topics? Read the docs here!