Question: Verify that ifc>0, then the function defined piecewise byy(x)={-(x-c)2,xc0,x>csatisfies the differential equation y'=2-y2 for all x. Sketch a variety of suchsolution curves for different values

Verify that ifc>0, then the function defined piecewise byy(x)={-(x-c)2,xc0,x>csatisfies the differential equation y'=2-y2 for all x. Sketch a variety of suchsolution curves for different values ofca and by'=2-y2,y(a)=b has. (Formore examples: 1.3, problems 27-33)

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