differential eqn dv/dt=g-4v: existence of limiting velocity

[res publica]

I need help with two problems:

The equation for the motion for a piece of metal is:

dv/dt = g-4v

find v and show that there is a limiting velocity

and: when is the piece of metal falling at g/10 m/s

Problem #2:

dV/dt = k(Vo - V) is the rate of evaporating water

in 20 days, 50% of the water evaporates; how much water (in percent) is remaining after 50 days?

Thanks for your help. It would be nice if you could give me a very easy to understand explanation of how this works. But if you can't, merely a solution is also helpful. Thanks for your support.

 

[royhaas]

Both of these can be written in the form: dy/(a-by)=dt. Integrate.