The transfer function of a certain circuit is given by

$G(s)=\frac{Y(s)}{x(s)}=\frac{N(s)}{s(s^2+2s+5)(s^2+4s+13)}$

Where $N(s)$ is an unspecified numerator polynomial. Using arbitrary constant magnitudes and phase angles, write the general form of the response $y(t)$ when a$)x(t)=10sin(2t)$ and b $)x(t)=10e^{-2t}.$ In each case identify the natural and forced components of the response. Discuss the steady$-$state response in each case. $($Note: it is assumed that $N(s)$ has no common roots with the denominator polynomials of $G(s)$ and $x(s)$