I am trying to find the capacitor voltage in the following picture:
Find i(t) in the figure below. Assume dc steady state conditions are valid for t<=0.
The Attempt at a Solution
At t<0 I found Vc to be 8 volts which should be correct according to the book. I am confused at the part after the switch is flipped though. I called the node between the two resistors and the capacitor "v" and used nodal analysis. So (v-4)/2 + v/2 + c(dv/dt)=0. I think my problem is that I am not accounting for the two ohm resistor that is in the branch with the capacitor, but I am not sure how to add that to my equation. My current equation gives me the wrong answer, any help would be appreciated. Oh and I'm trying to get a differential equation to solve, not sure what that method is called.