Use computer software to find the following:

a$.$ Expand each of the following s$-$domain functions into partial fractions:

i$.Y(s)=\frac{6s}{s^4-2s^3-64s^2+2s+63}$

ii$.Y(s)=\frac{7s^2}{s^4-8s^3+16s^2-8s+15}$

b$.$ Find inverse Laplace transforms for the previous functions, $y(t).$

c$.$ Find Laplace transform of the functions:

i$.y(t)=$Sin$(t)+t^2-2+e^{4-t}+S(t-5)Cos(6t-30)$

ii$.y(t)=\frac{t-2}{Csc(t+5)}$