Question: problem with piecewise and differentiate piecewise function

Dear all

I have an first-order ode

y'(x) =0, for x in [0,1] but x different to 1/2

and we define a function y(x)= 2   if 0<=x<0.5  and y(x)=0 for 0.5<=x <=1

The attached code define these function ( maybe piecewise function is not welle defined) and how can we show that y is solution or not of the differential equation

many thanks


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