(a) A direction field for the differential equation y' = x2 - y2 is shown. Sketch the solution of the initial-value problem y' = x2 - y2 y(0) = 1
Use the graph to estimate the value of y(0.3).


(b) Use Euler's method with step size 0.1 to estimate y(0.3), where y(x) 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?