Using wxMaxima to obtain a transfer function from T-twin filter & op amp
I think you have to add one more equation \$ \frac{\text{Vx}-\text{V1}}{R}+\mathcal{C} s (\text{Vx}-\text{V2}) == 0\$ and solve for \$V0\$ as well. Also your first equation needs to have the term \$ 2 \mathcal{C}\$ instead of \$ \mathcal{C}\$.

Computations using Mathematica.

sols = Solve[{
(V1 - Vi)/R + (V1 - Vx)/R + (V1 - V0) s 2 \[ScriptCapitalC] == 0, 
(V2 - Vi) s \[ScriptCapitalC] + (V2 - Vx) s \[ScriptCapitalC] + V2/(R/2) == 0, 
Vx == (RA V0)/(RA + RB), 
(Vx - V1)/R + (Vx - V2) s \[ScriptCapitalC] == 0}
, 
{V1, V2, Vx, V0}
];

tfm = TransferFunctionModel[V0/Vi /. sols[[1]] // Simplify, s]




Special cases:


\$RA = 0 \$, and any value of \$RB\$

tfm /. RA -> 0





\$RB = 0 \$, and any value of \$RA\$

tfm /. RB -> 0





\$R = 0 \$, and any value of \$\mathcal{C}\$

tfm /. R -> 0


\$\mathcal{C} = 0 \$, and any value of \$R\$

tfm /. \[ScriptCapitalC] -> 0




These are notch filters when \$\text{RA}&lt;\text{RB}\$.

values = {0.01, 0.1, 1, 10, 100, 1000};
Table[tfm /. {RA -&gt; 1, RB -&gt; 10, R -&gt; f/\[ScriptCapitalC]}, {f, values}];
BodePlot[%, PlotLayout -&gt; "Magnitude", PlotLegends -&gt; values]




They are still notch when \$\text{RA}&gt;\text{RB}\$.

Table[tfm /. {RA -&gt; 10, RB -&gt; 1, R -&gt; f/\[ScriptCapitalC]}, {f, values}];
BodePlot[%, PlotLayout -&gt; "Magnitude", PlotLegends -&gt; values, PlotRange -&gt; All]




If \$\text{RA}=\text{RB}\$, it turns out to be "all-pass" filters.

Table[tfm /. {RA -&gt; 1, RB -&gt; 1, R -&gt; f/\[ScriptCapitalC]}, {f, values}];
BodePlot[%, PlotLayout -&gt; "Magnitude", PlotLegends -&gt; values, PlotRange -&gt; All]