  We apply the method of comparison equations to study cosmological
perturbations during inflation, obtaining the full power spectra of scalar and
tensor perturbations to first and to second order in the slow-roll parameters.
We compare our results with those derived by means of other methods, in
particular the Green's function method and the improved WKB approximation, and
find agreement for the slow-roll structure. The method of comparison equations,
just as the improved WKB approximation, can however be applied to more general
situations where the slow-roll approximation fails.
