Transfer function of Operational Amplifier
I honestly don't see why using chained substitutions wouldn't do the trick. Don't have much time for pen-and-paper right now, but I'll show the matlab way do it.

syms Va Vn Vp Vi Vo G1 G2 G3 G4 G5 C1 C2 s

eq1 = (Va - Vn)*(s*C2) + (Va - Vp)*G3 + Va*G4;
eq2 = (Vn - Vi)*G2 + (Vn - Vo)*G1 + (Vn - Va)*(s*C2);
eq3 = (Vp - Va)*G3 + (Vp - Vi)*G5 + Vp*s*C1;
eq4 = Vp == Vn;

sol = solve([eq1, eq2, eq3, eq4],Va, Vp, Vn, Vo);
pretty(sol.Vo)


$$
\frac{V_o}{V_i} = \\ \frac{G_1 G_3 G_5 - G_2 G_3 G_4 + G_1 G_4 G_5 - C_1 G_2 G_3 s - C_1 G_2 G_4 s + C_2 G_1 G_5 s + C_2 G_4 G_5 s - C_1 C_2 G_2 s^2}{G_1(G_3 G_4 + G_3 G_5 + G_4 G_5 + C_1 G_3 s + C_1 G_4 s + C_2 G_5 s + C_1 C_2 s^2)}
$$