How to integrate this?

Homework Statement

How to integrate dv/dt=g-kv/m?

This is ODE.

The Attempt at a Solution

dv/(g-(kv/m))=dt
Now what? I don't know how to integrate the left side.

Mark44
Mentor

Homework Statement

How to integrate dv/dt=g-kv/m?

This is ODE.

The Attempt at a Solution

dv/(g-(kv/m))=dt
Now what? I don't know how to integrate the left side.
The left side can be rewritten as ##\frac{m \ dv}{mg - kv}##. There's a fairly obvious substitution you can use.

What substitution?

Never mind. I integrated and got (-m/k)ln abs(gm-kv)+C.

Now, how to simplify (-m/k)ln abs(gm-kv)=t+C?

Stephen Tashi
Are you saying you can't work $\int {\frac{1}{g- \frac{kv}{m}} }dv$ ?
Could you do something like $\int (3 -5v)^{-1} dv$ ?