A differential equation, a point, and a slope field are given. A slope field(or direction field) consists of line segments with slopes given by the differential equation. These line segments give a visual perspective of the slopes of the solutions of the differential equation. dy dx = − 1 x2 , x > 0, (1, 3)
(a) Sketch two approximate solutions of the differential equation on the slope field, one of which passes through the indicated point.
(b) Use integration to find the particular solution of the differential equation and use a
graphing utility to graph the solution. Compare the result with the sketches in part (a). dy/dx = -1/x², x > 0, (1, 3)