Your problem can be solved analytically.
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:
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 10=L \frac{dI}{dt}+IR+\frac{1}{C}\int I dt
or L\frac{d^Q}{dt^2}+I\frac{dQ}{dt}+\frac{Q}{c}=0

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=] RLC circuit simulation (DC Voltage source)[/url] to find out the simulated solution.