Assistance in checking transfer function

[incognitor]

Hi,

I am undertaking an undergrad design project and want to ensure I'm doing this correctly,

I have derived the ODE as shown below;

A*Y = M*X'' + (B+C)*X' + D*X
Where A,M,B,C,D are constants.

By taking the Laplace transform, I get;
A*Y(s) = M*s^2*X(s) + (B+C)*s*X(s) + D*X(s)

Therefore,
My transfer function becomes;

TF(s) = X(s)/Y(s) = the image of the transfer function below;
http://imageshack.us/a/img37/8820/95533304.jpg


Feedback on this would be much appreciated.

 

[X89codered89X]

It looks right, but I have 1 thing to ask
1) Is Input X and Y the output?

You should always have:

$Q(s)X_{out}(s) = P(s)X_{in}(s) \; \Rightarrow \; H(s) = \frac{P(s)}{Q(s)} = \frac{X_{out}(s)}{X_{in}(s)}$