Please provide detailed solution, not AI$-$generated. A system is described by the following differential equation:

a$.\frac{d^{3}y}{d{t}^3}+4\frac{d^{2}y}{d{t}^2}+8\frac{dy}{dt}+y=\frac{d^{3}x}{d{t}^3}+3\frac{d^{2}x}{d{t}^2}+5\frac{dx}{dt}+8x$

b$.2\frac{d^{2}y}{d{t}^2}+7\frac{dy}{dt}+10y=13\frac{d^{2}x}{d{t}^2}+15\frac{dx}{dt}+20x$

Find the expression for the transfer function of the

system, $Y\frac{s}{x}(s).$