Two commutation processes for RL circuit

[evol_w10lv]

I have to calculate first commutation process (t=0) and second commutation process (t = 2*τ)

Both swithes are closing in the given time moment as I wrote before.

I'll do this task step by step, that's why here isn't full of my own solution yet.
First of all, I want to ask few questions to be sure:

This is same circuit as before?
And then this is circuit of first commutation:

If it's true, I'll start to write equations for both commutations.

 

[Laplace]

Yes, an open switch in a series circuit effectively removes the components that are part of the open circuit, while a closed switch in a parallel circuit effectively removes the components that have been shorted.

 

[evol_w10lv]

Can you chek my solution or, actually, just result of first commutation?
I solved it, but I want to be sure about this result to continue with second commutation later.

 

[Laplace]

It appears to me that the answer obtained by inspection agrees with the answer derived from the differential equation.

 

[evol_w10lv]

Now I'm trying to solve second commutation.

I guess I have to use mesh current method with first loop and outside loop. Can you chek my result?

System looks complicate to solve it in mathematical way.. that's why not sure about my solution. Or it really should be complicated?
And what about initial condition for L2?