Question $2$

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A system is described by the following differential equation:

$6\frac{d^{4}y}{d{t}^4}+\frac{d^{2}y}{d{t}^2}-\frac{dy}{dt}+2y=2u+\frac{du}{dt}-2\frac{d^{2}u}{d{t}^2}$

Find the transfer function of the system Y$($s$)/$U$($s$)$

Select one:

a$.\frac{Y(s)}{U(s)}=\frac{-2s^2+s+2}{6s^4+s^2-s+2}$

b$.\frac{Y(s)}{U(s)}=\frac{-2s^2+s+2}{6s^3+s^2-s-2}$

c$.\frac{Y(s)}{U(s)}=\frac{-2s^2+s+2}{6s^3+s^2+s+2}$

d$.\frac{Y(s)}{U(s)}=\frac{-2s^2+s+2}{6s^3+s^2-s+2}$

e$.$ None of these