Time-dependent equations for coupled electron hopping and anion displacement are non-linear. For plane sheet solutions, the Boltzmann transformation is applicable at short times only. The general problem is treated by reducing the equation to classical form and investigating the concentration dependence of the coupled $ ̃ D and both t e and t x. For the cases D x⪢ D eand D e ⪢ D x we define a constant integral $ ̃ D avg and solve the concentration profiles in x and t. Local microfields enhance D e when D x ⪢ D e (e.g. $ ̃ D/ D e > 1) by local space charge generation in a classical way. Conversely, when D e ⪢ D x, the quantity $ ̃ D/ D x ⪢ 1 because the local field and concentration gradient of electrons operate in the same direction. For voltage steps, $ ̃ D applies at short times, but underestimates increasing values as concentration profiles develop. Solutions converge to expected anion mobility-independent steady state values.