Need help for making differential equations of following excercise
I think the issue is actually in the 3rd equation, which I believe should be:

\$ \Large  0 = V_o \times s \times C + \frac{V_o}{R_3} + \frac{V_o}{R_2} \$

or

\$ \Large 0 = V_o \times s \times C + 2 \times \frac{V_o}{R} \$ (if all Rs are the same)