RLC circuit - transfer function through differential equation - Band stop filter
You must raise the equilibrium equations of the circuit (applying LKV, LKC and Ohm's Law), and then apply the Laplace Transform, considering that the initial conditions must be zero.
Next, you must operate to find an expression for \$V_o(s)\$ depending on \$V_i(s)\$.

Then, the trasfer function is:

$$
G(s) = \dfrac{V_o(s)}{V_i(s)}
$$

Remember that

$$
L\quad\overset{\text{Laplace domain}}{\to}\quad s\cdot L\\
C\quad\overset{\text{Laplace domain}}{\to}\quad \dfrac{1}{s\cdot C}
$$