# (a) Identify the nullclines (see Problem 17) in Problems1, 3, and 4. With a colored pencil, circle...

## Question:

(a) Identify the nullclines (see Problem 17) in Problems€‘1, 3, and 4. With a colored pencil, circle any lineal elements in figures (1), (2) and (3) that you think may be a lineal element at a point on a nullcline.

(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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