A particle, of mass 2 kg, is dropped from rest and falls towards the ground. The resistance to motion is modelled by 5vN, where v is the velocity of the particle at any given time. The displacement of the particle, measured from the height where it is dropped, is denoted by x.

a. Show that the equation of motion is given by 2g – 5dx/dt = 2 d²x/dt², where g is the acceleration due to gravity.

b. Hence, using the initial conditions, find the particular solution of this differential equation, giving your answer in terms of g.