Determine transfer function from circuit with different currents
First thing I did was redraw the circuit. I added a node 'Vx' to help me solve.

(1)
$$I_1 = I_2 + I_3$$

(2)
$$I_1 = \frac{V_i - V_x}{R}$$

(3)
$$I_2 = (V_x - V_o) * sC$$

(4)
$$I_3 = \frac{V_x - V_o/u}{R}$$

Plugging equations 2,3,4 into 1 gives:

(5)
$$\frac{V_i - V_x}{R} = (V_x - V_o) sC +\frac{V_x - V_o/u}{R}$$

(6)
$$V_i = V_x (sCR + 2) - V_o(sCR + 1/u)$$

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Now let's get Vx in terms of Vo. I do this using I_3

$$I_{3 (R)} = I_{3 (C)}$$

$$\frac{V_x - V_o/u}{R} = (V_o/u) * sC$$

$$V_x = V_o * \frac{sCR}{u} + \frac{V_o}{u}$$

$$V_x = V_o * \frac{sCR+1}{u}$$

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Now, I have the rest done, but believe that you are capable of taking it from here. I think your roadblock was using Vx, which helped me get I1, I2, and I3.

Check your work by setting 'u' equal to 3, you should see some major magnitude peaking. For picture below I used R = 10kΩ, C = 1uF, u = 3.