RC Equation for 3rd order circuit

[Jaded1]

Hi guys, I'm working on some preparatory work for Fall term and I've come across this question in which I require some help.

 

I'm using the 3rd order Sallen-Key low-pass filter as in: http://sim.okawa-den...y3Lowkeisan.htm and I want to find the differential equation relating the output voltage (Vout) and input voltage (Vin).

 

Currently what I've done is split the circuit into 3 nodes from where I am think deducing the output voltage using kirchoffs circuit laws.

 

What I have for the above circuit is:

 

Va = (Va-Vin)/C1 + (Va-Vb)/R2 + (Va-Vout)/C2 = 0

 

Vb = (Vb-Va)/R2 + (Vb-Vout)/C2 + (Vb-Vc)/R3 = 0

 

Vc = (Vc-Vb)/R3 + (Vc-0)/C3 = 0

 

and since Vc = Vout, I am then going on to simply the equations. This is where I get stuck - how do I proceed from here (and is what I have done so far correct?)