We discuss the four exactly solvable problems: i) the diffusion of a particle in a time dependent parabolic potential, ii) the spatially restricted diffusion of a particle effected by a spatially homogeneous and time-dependent force, iii) the spatially restricted diffusion of two hard-core interacting particles driven by a spatially homogeneous and time-dependent force, iv) the dynamics of a molecular motor based on the externally driven two-level system and described by the Pauli master equation with the time-dependent transition rates.