The equations I have are
$\phi=(-ag/\omega)\cos(kx)\sin(\omega t)e^{kz}$
and
$\eta=a\cos(kx)\cos(\omega t)$
I know that $d\phi/dz=d\eta/dt$
but when I partially differentiate and rearrange I get
$gk e^{kz}= \omega^2$ and I don't know how to get rid of the exponential function.