The switch between capacitor and 2? opened at t=0, it means that the capacitor is charged to 12V*2/3=8V at t=0.

The problem reduced to RLC circuit with initial conditions:

t=0;

I=0, Vc=8V, V[sub]R[/sub]=0V, V[sub]L[/sub]=2V (V[sub]L[/sub]=10-Vc-V[sub]R[/sub] )

The differential equation need to be solved is

or

The solution is similar to a spring with constant k, attached with mass m and damping constant b.

The analytical solution can be found in standard textbook.

You are also welcomed to check out [url=http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=30.0] RLC circuit simulation (DC Voltage source)[/url] to find out the simulated solution.