The mathematical problem of transient currents that are produced by space-charge swarms after they are injected into liquids or gases is solved using a field-independent mobility model for the charge carriers. Only one species of charge carrier is assumed to be present in the fluid-containing drift space defined by parallel-plane constant potential electrodes. An integral-differential equation is derived for arbitrary initial charge distributions in the drift space. From its solution, the transient current waveform can be determined. When the initial current is in a steady state, the integral-differential equation reduces to a nonlinear ordinary differential equation which is valid for initial currents that mayor may not be space-charge limited. This final equation is solved for the special case of small space-charge fields. The analysis is also expected to apply to conduction in solids in some cases