op-amp difference amplifier

Letting Vi be the voltage at the op amp inputs, there are 2 node equations:

(Vi-V2)/R3 + (Vi-V3)/R4 + Vi/R5 = 0

(Vi-V1)/R1 + (Vi-Vo)/R2 = 0

Substituting to eliminate Vi gives:

((V1/R1 + Vo/R2)/(1/R1 + 1/R2))(1/R3 + 1/R4 +1/R5) = V2/R3 + V3/R4

Solving for Vo gives:

Vo= -V1(R2/R1)+(V2(R4R5(1+R2/R1))+V3(R3R5(1+R2/R1)))/(R3R4+R3R5+R4R5)

Did you start with the same node equations? I can't tell whether your Vo expression is the same as the one I derived. What desired ratios are you looking for?

 

If you will notice, my expression for Vo is in the form:
Vo= -cV1+bV2+aV3 where (if my derivation is correct),

c= (R2/R1)
b= (R4R5(1+R2/R1))/(R3R4+R3R5+R4R5)
a= (R3R5(1+R2/R1))/(R3R4+R3R5+R4R5)

Your task, after verifying the derivation, is to select values for R1, R2, R3, R4, & R5 that will make c=1, b=3, a=2, for your example. Good luck, it may not be possible to have "any values of a,b,c" since this circuit would normally be used in a configuration where a=b=c.