I have this circuit and I was asked to determine V2=f(V1) and V3=f(V2) which I determined below. The next step is to figure out what the purpose of this circuit is but I'm not sure how to do it from the equations I got.
The first op-amp is a differential amplifier set up to measure its common mode rejection ratio, and possibly its common mode input range.
The second op-amp is an inverting, dampened low pass filter. Real-world application is not known but possibly used to dampen a peak in the frequency response of the first op-amp.
It's hard to see what the first half of the circuit does. It could be a differential amplifier with the inputs tied together, depending on the res values. The second half is an inverting amplifier, as your equations show, with a pole at some frequency determined by C and R7 and a zero at a higher frequency determined by R6, R7 and C. So some sort of equaliser?