Twelve noncentral but separable potentials in cylindrical coordinates are solved by using supersymmetry algebra and shape invariant potential

the energy eigenvalues and the eigenfunctions are given analytically.Based on it and the results of one-dimensional time-dependent supersymmetric quantum mechanics

the time-dependent supersymmetry is generalized to higher dimensions

a method for solving noncentral but separable time-dependent potentials is formalized

six noncentral but separable time-dependent potentials in spherical coordinates have been solved

and other six ones in cylindrical coordinates have been worked out as well

the analytical expressions of the enery-eigenvalues and the wavefunctions are given explicitely.