  Making use of an ${\it ansatz}$ for the eigenfunctions, we obtain an exact
closed form solution to the non-relativistic Schr\"{o}dinger equation with the
anharmonic potential, $V(r)=a r^2+b r^{-4}+c r^{-6}$ in two dimensions, where
the parameters of the potential $a, b, c$ satisfy some constraints.
