Fluid level problem

Problem $3$

Consider a scenario where the height of a water surface in a container changes over time. Using the principle of conservation law of mass and the provided schematic diagram, complete the following questions:

$1.$ Derive the differential equation governing the height of the water surface as a function of time, based on the law of conservation of mass. Clearly state the variables and parameters involved in the equation.

$2.$ Solve the derived differential equation numerically using Matlab. Specify initial conditions for the water surface height as defined by a given custom scenario. Provide a plot of the water surface height as a function of time.