How to Derive the Transfer Function for a Circuit in LTspice?

[liquidFuzz]

I'm tinkering with a software called LTspice. The user can insert circuits and simulate them. After doing some Bode plots I started to wonder what the transfer function looked like. I usually don't bother about this when I build amplifiers, but this LTspice software got me curious.

I looked through some old note I have and came up with this, sort of.

H = Y/X
Where Y(s) is the laplace tranformation of y(t), likewise for x(t) and in-signal.
Impedance of a capacitor $Z_c = \frac{1}{i ω C}$ and the resistor $Z_R = R$. I guess the impedances should be written with $iω = s$ if a proper Laplace tranformation is to be done.

Can anyone show me how to derive Y and X for this circuit:

 

[liquidFuzz]

I forgot the inner resistance of the triode/tube. The inner resistance is between the input connection and the top/plate connection.

My fumbling attempts:
$\displaystyle X(s) = \frac{\frac{R_c+\frac{1}{sC}}{R_c \frac{1}{sC}}+R_c}{\left( \frac{R_c+\frac{1}{sC}}{R_c \frac{1}{sC}} \right)R_c}$


$Y(s) = \frac{R_c+\frac{1}{sC}}{R_c\frac{1}{sC}}+r_a$