# Homework Help: Lyapunov Stability

1. Nov 22, 2013

### motherh

A question I am doing hints that the solution (y,$\dot{y}$) = (0,0) of $\ddot{y}$ - $\frac{2}{t}$$\dot{y}$ + y = 0 is unstable. I believe (although I am not 100% sure) that is true however I am struggling to prove it.

I can rewrite the equation as a system of equations in matrix form to get

$\dot{x}$ = Ax + B(t)x,

where A = [{0,1},{-1,0}], B(t) = [{0,0},{0,$\frac{2}{t}$}].

This the form of all the theorems I appear to have. But all my theorems require me to find an eigenvalue of A with positive real part - which I can't here.

So basically have I made a mistake already or is there another theorem anybody knows of that can tell me the trivial solution is unstable?

2. Nov 23, 2013

Anybody?