A general linear response analysis is presented for investigating cosmic ray transients in interplanetary space. The diffusion equation for energetic particle transport in the solar wind is first linearized about a stationary configuration. The perturbation in the particle omnidirectional distribution function resulting from perturbations to the solar wind velocity, drift velocity, or spatial diffusion tensor corresponding to transient solar wind conditions may then be found by solving an inhomogeneous boundary value problem. As illustrative examples of the general analysis, transient perturbations in the cosmic ray number density due to variations in the spatial diffusion coefficients are computed in a one-dimensional solar wind based on the convection-diffusion equation, which disregards cosmic ray energy changes in the solar wind. Two variations are considered, corresponding to (1) a Forbush decrease arising from the passage of an interplanetary traveling disturbance (shock) and (2) the solar cycle variation arising from an 11-year sinusoidal variation of the spatial diffusion coefficient at the sun which then propagates out through the heliosphere. The predicted solar cycle variation exhibits a hysteresis effect in which high-energy particles lead low-energy particles and a time delay which increases with heliocentric distance within the inner heliosphere. The predicted Forbush decrease profiles exhibit precursors, precipitous decreases, and gradual approximately energy-independent recoveries arising from a decay of the propagating disturbance. The general feature of both variations are in accord with observations.