  Utilizing an appropriate ansatz to the wave function, we reproduce the exact
bound-state solutions of the radial Schrodinger equation to various exactly
solvable sextic anharmonic oscillator and confining perturbed Coulomb models in
$D$-dimensions. We show that the perturbed Coulomb problem with eigenvalue $E$
can be transformed to a sextic anharmonic oscillator problem with eigenvalue E.
We also check the explicit relevance of these two related problems in
higher-space dimensions. It is shown that exact solutions of these potentials
exist when their coupling parameters with $k=D+2\ell $ appearing in the wave
equation satisfy certain constraints.
