02:49
Calculus of a Single Variable
Slope Field In Exercises 47 and $48,$ a differential equation, a point, and a slope field are given.(a) Sketch two approximate solutions of the differential equation on the slope field, one of which passes through the given point. (To print an enlarged copy of the graph, go to MathGraphs.com.) Use integration and the given point to find the particular solution of the differential equation and use a graphing utility to graph the solution. Compare the result with the sketch in part (a) that passes through the given point.
$$\frac{d y}{d x}=\frac{1}{\sqrt{4 x-x^{2}}},\left(2, \frac{1}{2}\right)$$