Question: differentiate piecewise constant function

Hi all

When I solve using maple the first-order differential equation: diff(y,x)=0  for x in the closed interval [0,1] we obtain a constant function as a solution

but one can define the piecewise constant function see please the attached code

why when we differentiate the piecewise function gives undefined derivative at point zero and a half.

Whats is the relationship between this example and Existence and uniqueness theorem for fist order ode

Many thanks




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