Amechanical system is governed by the following differential equation what is the homogeneous solution
d^2y/dt^2 + 6 dy/dt + 9y = 4e^- t

The ODE has characteristic equation

with roots , and hence the characteristic solution

For the particular solution, assume an ansatz of , with derivatives

Substituting these into the ODE gives

so that the particular solution is

the equation for this situation is y=122+45. to solve the equation you would add 45 and 122 to get a total of 167lbs. in conclusion, grace's weight eight weeks ago was 167lbs.