For the following differential equations, compute the indicated transfer function(s). Assume zero initial conditions, express your answer as a rational function (ratio of two polynomials in s), and simplify as much as possible. (a) Find Y(s)/U(s) in: (b) Find Y(s)/U(s) in: y+az+ay+aoy = b+bu+bou. +a2+ a1+00 = 1, b+ b+b= y. (c) Find Y(s)/U(s) in: 12=23, a0x1+u, 23 -a223-0122 y=b2x3+b2+ box1. (d) Find Y(s)/U(s) in: = -a023 + bou, 221-0123 + bu, 23 22 0223 + bu, y = 23. (e) Find Z(s)/U(s) in: m + (b + b) + kz = ku + byu. (f) Find Zi(s)/Fa(s) and Z2(s)/Fa(s) in: m+b=fa+b22, bz2 + kz2 = b1. (g) Find Y(s)/U(s) in: (t) = x(7) x(T) dT, (t)+ax(t) = u(t). (h) Find X(s)/U(s) and Y(s)/U(s) in: y+y=x, x+x=u-y.