Please Solve!

Fro: in on The steady state of response of y(t) to a given forcing function x(t) is given by the solution to the homogeneous part of the differential equation, which is the solution to the equation without the forcing function term on the right-hand side. In this case, of the homogeneous equation is given by: d3y/(dt3)+20d2y/(dt2)+200dy/dt+500y=0 To find the steady state response yR(t), we need to solve for y(t) in the above homogeneous equation and then find the value of y(t) as t approaches infinity. This value is the steady state to response y_R(t). For the given forcing functions: (a) x(t)=5e(3t)cos(t10 deg ) The steady state response y_R(t) can be found by the solving the homogeneous equation and finding the value of y(t) as t approaches infinity. (b) x(t)=10cos(10t+20 deg ) The steady state response y_R(t) can be found in a similar manner as for the x(t)=5e(3t)cos(t10 deg). (c) x(t)=10e(t) The steady state response y_R(t) can be found in a similar manner as for x(t)=5e(3t)cos(t10 deg). (d) x(t)=10 The steady state response y_R(t) can be found in a similar manner as for x(t)=5e(3t)cos(t10 deg). It is important to note that the solution for y=R(t) for each of the given forcing functions may be the different and will require a separate solution for each case