According to the text book solutions, they used just three KCL(checked in blue color)s deriving each node voltages,
and I used five, by adding two more KCL(written in gray color and with arrows)s.
But, in my way, there's each one more answer for each Vo2 and Vo1, and they're wrong I think.
However, I have no idea about what's wrong with my two KCL(in gray)s.

p.s.: assume R3 = R4,
Vi2 = 5 + (1/2) * sin(wt), Vi1 = 5 - (1/2) * sin(wt) <- "V_commonmode = 5V, V_differential = sin(wt)"

 

According to the text book solutions, they used just three KCL(checked in blue color)s deriving each node voltages,
and I used five, by adding two more KCL(written in gray color and with arrows)s.
But, in my way, there's each one more answer for each Vo2 and Vo1, and they're wrong I think.
However, I have no idea about what's wrong with my two KCL(in gray)s.

p.s.: assume R3 = R4,
Vi2 = 5 + (1/2) * sin(wt), Vi1 = 5 - (1/2) * sin(wt) <- "V_commonmode = 5V, V_differential = sin(wt)"

Look very carefully at the nodes that you wrote your KCL equations for. Draw a circuit around the junction. Are you accounting for each of the currents that enter or leave those junctions.