Discrete Time Transfer to Difference Equation Conversion for Filter Implementation

I have carried out a bilinear transformation for the second order low pass filter:

y=(wn^2/s^2 + 2*zeta*wn*s+(wn)^2)*u

which resulted in:

y=((2.47+4.93z^-1+2.47z^-2)/(10.24-1.905z^-1+6.43z^-2))*u

At this stage I tried to convert back into difference equation format resulting in:

y=1.905yt-1 - 6.43yt-2 + 2.47ut + 4.93ut-1 + 2.47ut-2

I was then under the impression that these coefficients could be implimented into a filter using the convention:

y=a1 + a2 + b0 + b1 + b2

therefore, giving:

a= [1.905 -6.43]

b=[2.47 4.93 2.47]

as the parameters to use within the filter function however I have not had any luck implementing the filter in this way. Is this the correct methodology to use in the process of converting your discrete time transfer function (in terms of z^-1) back into a difference equation and finally implementing?

Thanks in advance,

Mike