Show that the differential equations y' = 3y/x and y' = x/3y define orthogonal families of curves;
Question:
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.
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