(a) A direction field for the differential equation y9 − x2 2 y2 is shown. Sketch the solution of the initial-value problem y9 − x2 2 y2 ys0d − 1 Use your graph to estimate the value of ys0.3d.

(b) Use Euler’s method with step size 0.1 to estimate ys0.3d, where ysxd is the solution of the initial-value problem in part (a). Compare with your estimate from part (a).

(c) On what lines are the centers of the horizontal line segments of the direction field in part

(a) located? What happens when a solution curve crosses these lines?

Transcribed Image Text:

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