Solve the differential equation (dy/dx)2 = 4y to verify the general solution curves and singular solution curve that are illustrated in Fig. Then determine the points (a, b) in the plane for which the initial value problem (y′)2 = 4y, y(a) = b has (a) no solution, (b) infinitely many solutions that are defined for all x, (c) on some neighborhood of the point x = a, only finitely many solutions.
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