Find the family of curves satisfying y' = x/y and sketch several members of the family. Then find the differential equation for the orthogonal family (see Exercise 63), find its general solution, and add some members of this orthogonal family to your plot.

Data From Exercise 63

Transcribed Image Text:

Show that the differential equations y'= 3y/x and y = -x/3y define orthogonal families of curves; that is, the graphs of solutions to the first equation intersect the graphs of the solutions to the second equation in right angles (Figure 15). Find these curves explicitly. FIGURE 15 Two orthogonal families of curves.