A cylindrical water tank $is$ draining through a small hole $at$ the bottom. According $to$ Torricelli's

Law, the rate $at$ which the water height $h(t)$ decreases $is$ proportional $to$ the square root $of$ the

water height:

$\frac{dh}{dt}=-k\sqrt[\phantom{2}]{h}$

where $k=0\mathrm{.}5\frac{m^{\frac{1}{2}}}{\text{m}\text{i}\text{n}}$ The initial condition $ish(0)=4m.$

$(a)$ Solve the differential equation. $(b)$ When $is$ the tank empty? $(c)Is$ the solution unique?

Justify your answer using Picard's Existence and Uniqueness Theorem.