Second order transfer function
To determine this transfer function, you have several options: use the brute-force approach or the fast analytical circuits techniques (FACTs). The first option uses KVL or KCL (for instance) but I have selected superposition as shown below:

Now, good luck to develop this expression and factor it in a meaningful way without making mistakes. The FACTs, on the other hand, ask you to determine the time constants of this circuit for a zeroed excitation and a nulled response. This is described in the book I wrote in 2016. By breaking the circuit in small individual sketches, you will get the final result in a clear and ordered form without writing a line of algebra:

Simply remove an energy-storing element and &quot;look&quot; through its connecting terminals to express the resistance \$R\$ you see. The time constant is then \$\tau=RC\$. If you follow the steps, this is what you have:

The response between the brute-force expression and that of the FACTs are rigorously similar as shown below: