Verify that if c is a constant, then the function defined piecewise bysatisfies the differ...

Verify that if c is a constant, then the function defined piecewise by

satisfies the differential equation y′ = 3y2/3 for all x. Can you also use the “left half” of the cubic y = (x − c)3 in piecing together a solution curve of the differential equation? Sketch a variety of such solution curves. Is there a point (a, b) of the Ay-plane such that the initial value problem y′ = 3y2/3, y(a) = b has either no solution or a unique solution that is defined for all x? Reconcile your answer with Theorem 1.