Course: Control Theory Qla. Given the following differential equation, solve for y(t) if all initial conditions are zero. U(S)=1/s day +12dy + 32y = 32u(1) dt2 dt b. Find the transfer function represented by| do(t) +2c(t) = r(1) dt c. Find the inverse laplace transform of the transfer function 3 G(s) (s 2)(s + 3)2 =