Transfer function in a 2L2C circuit
One way of seeing the question is that it demands for net conductance of the circuit. Which is inverse of net impedance offered by the circuit u/i1.
As i1 signifies net current drawn by ckt.
The following explanation is based on that methodology.
I assume you have to find transfer function of the=is ckt.
One simple method might be.


Replace Z by Laplace equivalents in circuit.
Find impedence(net) of the circuit. 
Znet = (sL)+inv(sC + inv(sL + 1/sC)) which is u/i1
Take inverse and you have your answer.


Just to warn nodal might go slightly long. Second is just adaptation of a visible fact(not too much of ideal nodal analysis)   it is  use (u-Va)/zl = i1 . Then you find Va interms of Z and u replace  it in this second eq. And then u should have ur answer. Hop this ans satisfies your query.