  Considering a model with Coupled Dilaton-Squared Curvature terms and a
dilatonic potential which replace the cosmological constant, we present an
analytic hyperscaling violating solution which is the generalization of
arXiv:1305.3279 for non zero $\theta$. We show that a specific coupling between
dilaton and the squared curvature terms produces a simple logarithmic behavior
for the dilaton. By imposing the null energy condition and stability
constraints, we investigate the allowed regions for the parameters of this
model. We then study the perturbations around $\mathrm{AdS_4} $ in the UV and
$\mathrm{\mathrm{AdS}_2\times \mathbb{R}^2} $ in the IR of the Einstein-Weyl
gravity which can support an intermediate hyperscaling violating solution in
order to resolve the $\mathrm{IR} $ singularity of the metric in 4d.
