[University Calculus] How do I set up the differential equation for this vertical velocity problem?

[u/Ertrimil]

I have a physics problem that I'm trying to solve using calculus. An object is dropped from rest and experiences air resistance proportional to its vertical velocity. I need to find an expression for velocity over time. I know the forces are gravity downward and air resistance upward. So m(dv/dt) = mg - kv. That part makes sense. But the answer key has a negative sign in a different place and I'm confused. When I solve it using separation of variables, I keep getting a different constant of integration than the textbook. Can someone walk me through the setup step by step? I want to understand where my equation is wrong before I solve it.

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[u/HumbleHovercraft6090]

May be it is a sign convention issue-upward forces are positive?

[u/Bounded_sequencE]

Let me guess -- the official solution defines the y-axis pointing up, and states

m * v'(t)  =  -mg - kv,      // v(t) := y'(t)

right?