  A procedure is presented for solving the Fokker-Planck equation with constant
diffusion but non-stationary drift. It is based on the correspondence between
the Fokker-Planck equation and the non-stationary Schr\"odinger equation. The
formalism of supersymmetric quantum mechanics is extended by applying the
Darboux transformation directly to the non-stationary Schr\"odinger equation.
From a solution of a Fokker-Planck equation a solution of the Darboux partner
is obtained. For drift coefficients satisfying the condition of shape
invariance, a supersymmetric hierarchy of Fokker-Planck equations with
solutions related by the Darboux transformation is obtained.
