Since a constant current source is present, the output voltage will always be $$V_o=i_sR_f$$
However, you can also drive $$i_s=i_c+i_R=C\frac{dv_c}{dt}+v_c/R$$
Then you can say that the output voltage is a function of capacitor voltage and is an exponential function.
The two approaches seem contradictory. Which one is correct? Is the output voltage constant or not? Why?