I have the following circuit:

I have to find the transfer function by using mesh analysis. First of all I used the Laplace transformation.
  Although i saw some similar exercises, i don't really see what I can get out of the mesh equations.

1st Mesh $$V(s) - I_{1}(s)R_1 - V_{L_1}(s) = 0$$

2nd Mesh $$V_{L_1}(s) - I_{2}(s)R_2 - I_{2}L_{2}s = 0$$

Also I assumed that $$V_{L_1}(s) = sL_{1}(I_{1}(s) - I_{2}(s))$$

I would be thankful for any help

I have the following circuit:

I have to find the transfer function by using mesh analysis. First of all I used the Laplace transformation. 

Although I saw some similar exercises, I don't really see what I can get out of the mesh equations.

1st Mesh $$V(s) - I_{1}(s)R_1 - V_{L_1}(s) = 0$$

2nd Mesh $$V_{L_1}(s) - I_{2}(s)R_2 - I_{2}L_{2}s = 0$$

Also I assumed that $$V_{L_1}(s) = sL_{1}(I_{1}(s) - I_{2}(s))$$