A linear time$-$invariant system is given by

$\frac{d^{2}y(t)}{d{t}^2}+6\frac{dy(t)}{dt}+25y(t)=\frac{dx(t)}{dt}+3x(t)$

Its initial condition is $y(0)=0$ and $dy\frac{0}{d}t=2.$

a$)$ Calculate the zero$-$input response of this system.

b$)$ Determine the stability of the system. Justify your answer.