There are three conditions:
- before the switch is closed (opened)
- while the switch is closed (closed)
- after the switch is closed (opened)
I think I need to solve them sequentially, because the system has memory.
Here are the system equations (before the switch is closed):
Also, the current flow of \$V2\$ before the switch is closed is meaningless; if I try to cut the wire between \$V2\$ and node \$a\$ to see the graph before and after, it won't alter \$V_c\$ and \$V_d\$. So it is meaningless. That's why I'm not including this current flow in the equation number 1 above.
Edit: Sorry, it did alter, but for a tiny amount
Some strange things happened after plugging in the \$R\$ values. When I use Microsoft Mathematics to solve equations \$2\$ and \$3\$, I get the correct graph, but if I try to solve the equation \$2\$ with \$1\$, or \$3\$ with \$1\$, I get the wrong graph. What's wrong?