4.2 The differential equation for 10^3 < Re < 10^5
The magnitude of the drag force is k2 v^2. For an upwardly moving sphere, the velocity is positive, so the drag force should be negative.
m dv/dt = -m g - k2 v^2
For a downwardly moving sphere, the velocity is negative, so the drag force should be positive.
m dv/dt = -m g + k2 v^2
Up to 4. The Differential Equations for a Sphere Moving through a Fluid