Here is a first-order op-amp circuit:
I have to find V0 given that V(0) = 4 V (i.e. the capacitor is charged). If the capacitor is charged, then the voltage at the node 1 is V1 = 4V and KCL must look something like this: $$ \frac{0 - V_1}{R_1} = C\frac{dV}{dT} + \frac{V_1 - V_0}{R_f} $$ However, the solution postulates that since the node 2 has a zero voltage, then V1 = 0. It seems that there is some contradiction. Does the voltage on the capacitor influences the voltage of the node 1 or not? I have studied op-amp theory, however, I feel perplexed because university curriculum and textbooks takes onto consideration only two cases: either the voltage source is between the ground and the inverting input or it is between the ground and the non-inverting input. This is the first time when I see such a circuit that's why I have posted this question.