Chapter 8.2, Problem 16P

By separation of variables, find a solution of the equation $y^{\prime }=\sqrt{y}$ containing one arbitrary constant. Find a particular solution satisfying $y=0$ when $x=0.$ Show that $y\equiv 0$ is a solution of the differential equation which cannot be obtained by specializing the arbitrary constant in your solution above. Computer plot a slope field and some of the solution curves. Show that there are an infinite number of solution curves passing through any point on the $x$ axis, but just one through any point for which $y>0.$ Hint: See Example 3. Problems 17 and 18 are physical problems leading to this differential equation.