(a) Verify that if c is a constant, then the function defined piecewise bysatisfies the di...

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

satisfies the differential equation , for all x (including the point x = c). Construct a figure illustrating the fact that the initial value problem , y(0) = 0 has infinitely many different solutions.

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(b) For what values of b does the initial value problem , y(0) = b have (i) no solution, (ii) a unique solution that is defined for all x?