How do i solve a circuit when a capacitor is between in op amp inputs?
You'll have to assume a finite gain for the op-amp (meaning the voltage between the inputs is small, but not zero), and preferably also a non-zero impedance for the reference diode to get a sensible answer.
The main reason for using this configuration is to prevent small DC shifts due to EMI, especially with a bipolar input op-amp, which should be a hint that a linear approximation is insufficient to fully analyze it.