Filter Network - (answer does not match books)

[FrogPad]

I'm not sure what I'm doing wrong here, as my answer does not match up with the books. Sorry about the scan, it looks kinda bad.

! I made a mistake writing the books answer down. It should be:

$$\bar G_v(j \omega ) = \frac{j \omega C (R_1+R_2)+1}{j \omega R_1 +1}$$
Any help would be awesome! Thanks!

 

[Rumpelstiltzkin]

You sure it's not:

$$\bar G_v(j \omega ) = \frac{j \omega C (R_1+R_2)+1}{j \omega C R_1 +1}$$

Anyway, I think your nodal equation is incorrect. KCL states that the sum of all currents flowing out of the node equals to zero. Vi/a and (Vi-Vo)/b are both currents flowing out of the node. So it's supposed to be Vi/a + (Vi-Vo)/b = 0.

 

[FrogPad]

slapping myself in the head

Thanks Rumpelstiltzkin !