(a) Identify the nullclines (see Problem 17) in Problems1, 3, and 4. With a colored pencil, circle...
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(b) What are the nullclines of an autonomous first-order DE?
(1)
(2)
(3)
Data from problem 17
For a first-order DE dy/dx = f (x, y) a curve in the plane defined by f (x, y) = 0 is called a nullcline of the equation, since a lineal element at a point on the curve has zero slope. Use computer software to obtain a direction field over a rectangular grid of points for dy/dx = x2 - 2y, and then superimpose the graph of the nullcline y = 1/2 x2 over the direction field. Discuss the behavior of solution curves in regions of the plane defined by y < ½ x2 and by y > ½ x2. Sketch some approximate solution curves. Try to generalize your observations.
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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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