differential equation

[royal robin]

I would like to find the function v

[grizzled crag]

Let's see.
dv/dt = kv^2 - g
You did the separation of variables correctly, so:
dv/(kv^2 - g) = dt
Now, consider that kv^2 - g = (√(k)v - √(g))(√(k)v + √(g)). So, use partial fractions on the left part to arrive at some elemetary integrals.

[royal robin]

Ok I will try now thanks