The differential equation dx/dt = 100x(x- 5)+ s models a population with stocking at rate s. Determine the depen- dence of the number of critical points c on the parameter s, and then construct the corresponding bifurcation diagram in the sc-plane.

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A: hintddxtan-1x=11+x2 or,∫11+x2dx=tan-1x

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A: We can apply fundamental theorem of calculus here.  The second fundamental theorem of calculus…

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A: The figure as,

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A:

Q: a) How is ds/dt related to dx/dt if y is constant? ds/dt=___(dx/dt)

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A:

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A: Solve for the differentiation

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A: