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

## Question:

(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 = x^{2} - 2y, and then superimpose the graph of the nullcline y = 1/2 x^{2} over the direction field. Discuss the behavior of solution curves in regions of the plane defined by y < ½ x^{2} and by y > ½ x^{2}. Sketch some approximate solution curves. Try to generalize your observations.

Fantastic news! We've Found the answer you've been seeking!

## Step by Step Answer:

**Related Book For**

## A First Course in Differential Equations with Modeling Applications

**ISBN:** 978-1305965720

11th edition

**Authors:** Dennis G. Zill