The question is:
Is there any function $\phi$ such that the system dfined by equations $$\dot{x}=-\sinh{x}\\ \dot{y}=-y\cosh{y}+x\phi(y)$$ has an asymptotically stable equilibrium point in the origin?
I think I should use LaSalle's theorem but I don't know how to find a proper potential function $V$ for this purpose.
Any help is appreciated.