Given the system
a) Find the equilibrium
b) Show that if ab-lk does not equal 0, the steady state found in (a) is the only solution
c) choose a,b,l,k such that ab-lk > 0. Find numerically the solution of the system starting in a neighborhood of the equilibrium.
2. The attempt at a solution
a) If x'(t)=y'(t)=0, then ax(t)=ky(t) and lx(t)=by(t). This is true for ab = lk, i.e. ab-lk=0.
and then I run into trouble. I don't know how to explicity show (b), and have even less of an idea on how to start (c)