Solution
= Solution
<Neutrino free streaming> gives $\delta_\nu\simeq0$ on the stated scales, so $\delta_m=(1-f_\nu)\delta_{cb}$. With derivatives with respect to $N=\log a$, the growth equation becomes
$$
\delta_{cb,NN}+\frac12\delta_{cb,N}
-\frac32(1-f_\nu)\delta_{cb}=0.
$$
For $\delta_{cb}\propto a^p$,
$$
p=\frac{-1+\sqrt{25-24f_\nu}}4
=1-\frac35f_\nu+O(f_\nu^2).
$$
Hence
$$
\boxed{X(f_\nu)=1-\frac35f_\nu}
$$
to first order.