Find a Liapunov function of this linear system

Question

I'm trying to study the behavior of equilibrium point in the origin of the linear system associated with this matrix:
$$ A= \begin{pmatrix} 0 & 1 \\ 0 & 0 \\ \end{pmatrix} $$

The eigenvalues are $\lambda_1=\lambda_2=0$, since they aren't negative, we know that this system is not asymptotically stable.

I'm trying to find a Liapunov function to prove this system is stable, but I couldn't find it.

I need help.

Thanks a lot.

Answer 1

Hint: This system is solved explicitely by $(x(t),y(t))=(x(0)+y(0)t,y(0))$. (Un)stability of the equilibrium point $(0,0)$ follows by inspection.