= Solution
For an <Einstein-de Sitter universe>, $H=\dot a/a=2/(3t)$. The flat matter-only <Friedmann equation> $H^2=8\pi G\rho_m/3$ gives $\rho_m=1/(6\pi Gt^2)$. With zero <sound speed> the perturbation equation is therefore
$$
\ddot\delta_k+\frac4{3t}\dot\delta_k-\frac2{3t^2}\delta_k=0.
$$
Substituting $t^s$ yields $s(s-1)+4s/3-2/3=0$, or $(3s-2)(s+1)=0$. Hence
$$
\boxed{\delta_k=A_kt^{2/3}+B_kt^{-1}},
$$
with growing mode proportional to the <scale factor> and decaying mode proportional to $t^{-1}$.
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