  Any second order homogeneous linear ordinary differential equation can be
transformed into a first order non-linear Riccati equation. We argue that the
Riccati form of the linearized fluctuation equations that determine the
holographic 2-point functions simplifies considerably the numerical computation
of such 2-point functions and of the corresponding transport coefficients by
computing directly the response functions, eliminating the arbitrary source
from the start. Moreover, it provides a neat criterion for the infrared
regularity of the fluctuations. In particular, it is shown that the infrared
regularity conditions for scalar and tensor fluctuations coincide, and hence
they are either both regular or both singular. We demonstrate our numerical
recipe based on the Riccati equations by computing the holographic 2-point
functions for the stress tensor and a scalar operator in a number of
asymptotically anti de Sitter backgrounds of bottom up scalar-gravity models.
Analytical results are obtained for the 2-point function of the transverse
traceless part of the stress tensor in two confining geometries, including a
geometry that belongs to the class of IHQCD. We find that in this background
the spin-2 spectrum is linear and, as expected, the position space 2-point
function decays exponentially at large distances at a rate proportional to the
confinement scale.
