Keep both sides of a terminal velocity when separating

[Motion of Particles with Resistance]

Modified from Fundamentals of Differential Equations and Boundary Value Problems, sixth edition, p110. An object starts with velocity v0 and falls under gravity $g=9.81$ metres per second squared. Air resistance gives deceleration proportional to velocity. Given $dv/dt=g-kv$, $k>0$, express v in terms of t.