how to solve this question?

7.4 In the lecture notes (or online video) we saw that for a particle of mass m placed on the surface of a pot of honey, the vertical z coordinate of the particle satisfies the ODE mz=zmg where g is the acceleration due to gravity and >0 is a constant. (a) Solve this equation for z(t) with the initial conditions that the particle starts at rest from the surface of the honey, which we define to be the origin: z(0)=0,z(0)=0 (b) Assume that the honey occupies an infinitely deep well. What is the limiting value of z as t ? This is called the terminal velocity of the particle. Set m=g==1 for simplicity, and sketch the graph of z(t), showing the asymptotic behaviour of z(t) as t