Consider the following system differential equation: d+y(t) dy(t) dt3 dt4 +5 7 dy(t) dt +36 dy(t) dt - 100y(t) b) Find the transfer function for the system, G(s) = = du(t) dt + 5u(t) a) Find the Laplace transform of the ODE, assuming zero initial conditions. Y(s) U (s)* c) Find the Laplace transform for the output, Y(s), if the input is u(t) = sin(6t). Note: It is okay to express you answer as the multiplication of several polynomials; no need to expand.