= Solution
For a $1\ \mathrm{Mpc}$ mode, evolve the regular superhorizon <density contrast> as $\delta\propto a^2$ until <cosmological horizon entry>. In the <radiation domination> approximation its entry scale is $a_{\rm ent}\simeq(H_0R/c)\sqrt{\Omega_\gamma}=2.2\times10^{-6}$, well before <matter-radiation equality>. At that point use the <Mészáros equation> basis of <6/d>, fixing both constants by continuity of $\delta$ and $\dot\delta$, equivalently $\delta$ and $d\delta/d\ln a$.
Explicitly, for entry data $\delta_e$ and $\delta'_e=2\delta_e/y_e$, solve
$$
\begin{pmatrix}D_1(y_e)&D_2(y_e)\\D_1'(y_e)&D_2'(y_e)\end{pmatrix}
\begin{pmatrix}A_1\\A_2\end{pmatrix}
=\begin{pmatrix}\delta_e\\2\delta_e/y_e\end{pmatrix}.
$$
The nonzero <Wronskian> guarantees a unique match. This produces slow logarithmic growth before equality, then $\delta\propto a$ with a decaying transient after equality. For example, at $y_e\ll1$, $A_2\simeq-2\delta_e$ and $A_1\simeq\delta_e+2\delta_e[\ln(4/y_e)-3]$. An abrupt match estimates the growth history; a precise amplitude requires a common gauge and the coupled relativistic perturbation equations through entry. Linear evolution also ceases to apply once $|\delta|$ approaches unity, and late <dark energy> further suppresses growth.
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