Suppose that y(x) is a nonconstant solution of the autonomous equation dy/dx = f (y) and that
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Suppose that y(x) is a nonconstant solution of the autonomous equation dy/dx = f (y) 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 40? Why can’t y(x) be oscillatory or have a relative extremum (maximum or minimum)?
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Recall that for dydx f y we are assuming that f and f are continuous functions of y on some i...View the full answer
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Related Book For 
A First Course in Differential Equations with Modeling Applications
ISBN: 978-1305965720
11th edition
Authors: Dennis G. Zill
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