  By applying an ansatz to the eigenfunction, an exact closed form solution of
the Schr\"{o}dinger equation in 2D is obtained with the potentials,
$V(r)=ar^2+br^4+cr^6$, $V(r)=ar+br^2+cr^{-1}$ and
$V(r)=ar^2+br^{-2}+cr^{-4}+dr^{-6}$, respectively. The restrictions on the
parameters of the given potential and the angular momentum $m$ are obtained.
