- #1

kreil

Gold Member

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## Homework Statement

Given the system

[tex]x'(t)=-ax(t)+ky(t)+g[/tex]

[tex]y'(t)=lx(t)-by(t)+h[/tex]

If g=h=0,

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)

Help!

Josh