Suppose that y(x) is a nonconstant solution of the autonomous equation and that c is a critical point of the DE. Discuss. Why can’t the graph of y(x) cross the graph of the equilibrium solution y = c? Why can’t f ( y) change signs in one of the subregions discussed on page 38? Why can’t y(x) be oscillatory or have a relative extremum (maximum or minimum)?
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