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How did this ratio come from the problem of university circuits?
To correct your ambiguity, this is not a second-order circuit, but a first-order rc circuit, which is suitable for the three-factor method.

The initial value of capacitance is difficult to calculate. Theoretically, the voltage of the capacitor can't suddenly change, but when two capacitors are connected in parallel, the voltage on the capacitor may suddenly change. What is the voltage after the mutation? Didn't the teacher teach? Let me remind you that matter does not die, right? The charge will not disappear naturally. In the past, both capacitors had energy storage, so they both had charge. Now it has become a capacitor inflow, and the original charge number remains unchanged. What should the current and voltage be? You can do the math yourself. You can continue to ask questions if you have any questions.