1. (a) Torricelli's law implies that the time rate of change (the rate of change with respect to time, t) of the volume, V of water in a draining tank is proportional to the square root of the depth, y, of the water in the tank. Write down the associated differential equation. (b) Further, if the tank is a cylinder with vertical sides and cross-section area A then V = Ay. Use this substitution in part (a) to find the depth of water in the tank at any later time.