Problem $4$: A system is described by the following differential equation:

$\frac{d^{3}y}{d{t}^3}+5\frac{d^{2}y}{d{t}^2}+2\frac{dy}{dt}+y=8\frac{d^{2}x}{d{t}^2}+6\frac{dx}{dt}+x$

$\frac{d^{2}y}{d{t}^2}+3\frac{dy}{dt}+4y=2x$

Find the expression for the transfer function of the system and determine the impulse response.