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**The problem is:**

A snowball is dropped from the top of a building, evaporation causes the mass

*m*of the snowball to decrease at a rate proportional to the snowball's speed as the snowball falls, so that

M' = k * abs(y')

where y denotes the vertical distance from the ground and

*k*is a negative constant.

Derive the differential equation governing

*y(t)*, neglecting all physical phenomena except the pull of Earth's gravity on the snowball and the variation in the snowball's mass

__This is what I have been able to work out:__

v = d/dt(position) = y'(t)

Using newtons Second law

Net force = (d/dt)[(mass)(velocity)]

-m(t)g = (d/dt)(m(t)y'(t))

-m(t)g = m'(t)y'(t)+m(t)y''(t)

And I'm not able to simplify this expression so I must be missing something in the setup...Any help would be great.