I have the following circuit:

[![enter image description here][1]][1]

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

[![enter image description here][2]][2]

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 $$V_{L_1}(s) = sL_{1}(I_{1}(s) - I_{2}(s))$$


  [1]: https://i.sstatic.net/PlseI.png
  [2]: https://i.sstatic.net/bGARd.jpg