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SOLVED:Verify that if c is a constant, then the function defined piecewise by y(x)={ 1 if x ≦ c, cos (x-c) if c<x<c π -1 if x ≧ c π. satisfies the differential equation y^'=-√(1-y^2) for all x. (Perhaps a preliminary sketch with c=0 will be helpful.) Sketch a variety of such solution curves. Then determine (in terms of a and b ) how many different solutions the initial value problem y^'=-√(1-y^2), y(a)=b has.
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