= Solution
For an <adiabatic cosmological perturbation>, the baryon and photon fractional density perturbations obey $\delta_b=3\delta_\gamma/4$. Since the pressure of the <photon-baryon fluid> is supplied by the photons,
$$
dP=\frac13d\bar\rho_\gamma,
\qquad
d\bar\rho=d\bar\rho_\gamma+d\bar\rho_b
=\left(1+\frac{3\bar\rho_b}{4\bar\rho_\gamma}\right)d\bar\rho_\gamma.
$$
The <photon-baryon sound speed> is therefore
$$
\boxed{c_s=c\sqrt{\frac{dP}{d\bar\rho}}
=\frac c{\sqrt3}\left(1+\frac{3\bar\rho_b}{4\bar\rho_\gamma}\right)^{-1/2}.}
$$
Use $\bar\rho_b\propto a^{-3}$ and $\bar\rho_\gamma\propto a^{-4}$ in the <Comoving Jeans length>
$$
\lambda_{J,{\rm com}}=\frac{c_s}{a}\sqrt{\frac\pi{G\bar\rho_b}}.
$$
Well before <matter-radiation equality>, photon inertia dominates, $c_s\simeq c/\sqrt3$, and
$$
\lambda_{J,{\rm com}}\propto a^{1/2}\propto t^{1/4}.
$$
Once baryon loading dominates while <tight coupling> still holds, $c_s\propto a^{-1/2}$, so $\lambda_{J,{\rm com}}$ is approximately constant. At <cosmological recombination>, photon pressure support disappears and the baryonic Jeans scale drops sharply. For a subsequently adiabatic monatomic gas, $T_b\propto a^{-2}$ and $c_s\propto a^{-1}$, giving
$$
\lambda_{J,{\rm com}}\propto a^{-1/2}\propto t^{-1/3}
$$
in an <Einstein-de Sitter universe>. The requested graph therefore rises as $t^{1/4}$, flattens before recombination, jumps downward there, and then decreases as $t^{-1/3}$.
For collisionless matter, the same instantaneous estimate uses its one-dimensional <velocity dispersion> $\sigma_v$ instead of $c_s$; more precisely, suppression is described by <collisionless free streaming>. Thus
$$
\lambda_{J,{\rm com}}\sim\frac{\sigma_v}{a}\sqrt{\frac\pi{G\bar\rho_{\rm cdm}}}.
$$
While the particles are relativistic, $\sigma_v\simeq c$ and $\lambda_{J,{\rm com}}\propto a^{1/2}$. Once nonrelativistic but thermally coupled to radiation, $T_{\rm cdm}\propto a^{-1}$, so $\sigma_v\propto a^{-1/2}$ and the scale is constant. After kinetic decoupling, momentum redshifts as $a^{-1}$, so $\sigma_v\propto a^{-1}$ and $\lambda_{J,{\rm com}}\propto a^{-1/2}$. The second graph joins these three power laws at $t_{\rm NR}$ and $t_{\rm dec}$; unlike the baryonic graph, its final decline begins at dark-matter kinetic decoupling rather than recombination.
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