Question: (a) Sketch a direction field for the differential equation y = x/y. Then use it to sketch the four solutions that satisfy the initial conditions

(a) Sketch a direction field for the differential equation y’ = x/y. Then use it to sketch the four solutions that satisfy the initial conditions y (0) = 1, y (0) = – 1, y (2) = 1 and y (– 2) = 1.
(b) Check your work in part (a) by solving the differential equation explicitly. What type of curve is each solution curve?

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