The relationship between the input x(t) and the output y(t) of a system is $$\frac{{{d^2}y}}{{d{t^2}}} = x\left( {t - 2} \right)u\left( {t - 2} \right) + \frac{{{d^2}x}}{{d{t^2}}}$$
The transfer function of the system is

A. $$1 + \frac{{{s^2}}}{{{e^{2s}}}}$$

B. $$1 + \frac{{{e^{ - 2s}}}}{{{s^2}}}$$

C. $$1 + \frac{{{e^{2s}}}}{{{s^2}}}$$

D. $$1 + \frac{{{s^2}}}{{{e^{ - 2s}}}}$$

Answer: Option B