Last week I took my semester Electric Circuit exam. I stuck with a question. I attached its picture below.
It asked the voltage difference between both sides of the switch at t=1.
I tried to solve it but the answer I found was from first-order which I think it's wrong. May you explain it?

 

You need to show your best effort at solving the problem so that we can see where you are going right and where, if anywhere, you are going astray.

Since you haven't labeled your diagram but think that this is sufficient for us to answer your question, I'm guessing that your work on the exam didn't amount to much. If so, that's fine. But now you have the time needed to make a more serious effort.

When you say you want the voltage at t=1, t=1 what? 1 second? 1 day? 1 microsecond? 1 month? Units matter.

 

I wasted at least 40 minutes for it at the exam.
t=1 means at the equation put t equals 1. t=1 second.
As far as I remember the answer equation I found was something like Ae\(^{Bt}\)-Ce\(^{Dt}\). A,B,C,D are coefficients.
If the answer isn't from first order then tell me to solve it again.

 

If the answer isn't from first order then tell me to solve it again.

Okay. Solve it again.

It's inherently a second-order system.