Output Resistance Voltage Controlled current source
(1) You already have the (closed loop) open circuit output voltage as a function of the input voltage.

Place a short across the output and solve the short circuit output current as a function of the input voltage.

The ratio of these is the output resistance:

\$R_{out} = \dfrac{\frac{V_{O(oc)}}{V_i}}{\frac{I_{O(sc)}}{V_i}}\$

(2) Zero the input voltage, connect a unit test current source to the output and solve for the output voltage due to the test source.  This will give you the output resistance directly.




  Just released Ve should be zero, because Vi is zero, because we
  haven't applied any input voltage to circuit.


For method (2), since the input voltage is zero, the output voltage is simply:

\$V_o = I_{test}R_{out}\$

But:

\$V_\epsilon = V_i - kV_o = -kV_o\$

By KVL:

\$V_o = I_{test}r_o + AV_\epsilon = I_{test}r_o - AkV_o \$

so:

\$V_o = I_{test} \dfrac{r_o}{1 + Ak} = I_{test} R_{out}  \$