= Solution
Current conservation at A, with the <capacitor> $C_1$ connected from A to the output as verified in the PDF, gives
$$
\frac{V_{\rm in}-V_A}{R_1}
=\frac{V_A-V_B}{R_2}+sC_1(V_A-V_{\rm out}).
$$
Substitute $V_A=(1+sR_2C_2)V_B$ and $V_{\rm out}=KV_B$:
$$
\frac{V_{\rm in}}{V_B}
=1+s[C_1R_1(1-K)+C_2(R_1+R_2)]+s^2R_1R_2C_1C_2.
$$
Therefore, at $s=i\omega$,
$$
\boxed{\frac{V_{\rm out}}{V_{\rm in}}
=\frac K{1-\omega^2R_1R_2C_1C_2+i\omega[C_1R_1(1-K)+C_2(R_1+R_2)]}}.
$$
This algebraic <transfer function> alone does not establish that transients decay; the <pole> check in the parent solution is necessary for the requested numerical choice.
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