In many of the theories of prediction and detection developed during the past decade, one encounters linear integral equations which can be subsumed under the general form

. This equation includes as special cases the Wiener-Hopf equation and the modified Wiener-Hopf equation

. The type of kernel considered in this note occurs when the noise can be regarded as the result of operating on white noise with a succession of not necessarily time-invariant linear differential and inverse-differential operators. For this type of noise, which is essentially a generalization of the stationary noise with a rational spectral density function, it is shown that the solution of the integral equation can be expressed in terms of solution of a certain linear differential equation with variable coefficients.