Problem$5$

Reconsider the previous problem of flow in a water reservoir. In order to control the level of water in

the reservoir, and avoid overflow that may flood the surrounding areas, a pump is used to remove water

from the reservoir.

An automatic control valve coupled with a sensor allows to adjust the output flow rate by the pump

such that it varies with the level of water in the reservoir; $q_0=.h(t)$ where $$ has units of $\frac{m^2}{s}.$

Determine how the level of water varies when the pump is used. Assume again that the reservoir is

initially empty.