Homework Help is Here – Start Your Trial Now!
Math
Calculus
. Shown at right is the slope field for which differential equation? A. dy= B. Jax 11 US // 1 -1/ 1 111 11 1 //

. Shown at right is the slope field for which differential equation? A. dy= B. Jax 11 US // 1 -1/ 1 111 11 1 //

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question

Hey! I'm having a little difficult answering this problem!

### Differential Equations and Slope Fields #### Question **(4.) Shown at right is the slope field for which differential equation?** #### Multiple Choice Options: - **A.** \(\frac{dy}{dx} = \frac{x^2}{y}\) - **B.** \(\frac{dy}{dx} = \frac{x^3}{y^2}\) - **C.** \(\frac{dy}{dx} = \frac{x^3}{y}\) - **D.** \(\frac{dy}{dx} = \frac{x^2}{y^2}\) (NOTE: Option **C** has been marked as the correct answer.) #### Explanation of the Slope Field Graph The graph on the right is a slope field (or direction field) that visually represents the slopes of a differential equation at various points \((x, y)\) on the plane. Each small segment or line in the field indicates the slope of the solution curve at that specific point. The slope field provides an intuitive way to see the behavior of solutions to differential equations without solving the equation analytically. The horizontal axis represents the \(x\)-coordinate, and the vertical axis represents the \(y\)-coordinate. **Key Features to Note:** 1. The slope lines vary in direction and steepness across different points. 2. As \(x\) and \(y\) values change, the slope of the lines adjusts accordingly, representing the differential equation's behavior. This specific slope field corresponds to the differential equation \(\frac{dy}{dx} = \frac{x^3}{y}\). This is validated by observing the pattern of the lines' slopes and matching it with the given options.
Transcribed Image Text:### Differential Equations and Slope Fields #### Question **(4.) Shown at right is the slope field for which differential equation?** #### Multiple Choice Options: - **A.** \(\frac{dy}{dx} = \frac{x^2}{y}\) - **B.** \(\frac{dy}{dx} = \frac{x^3}{y^2}\) - **C.** \(\frac{dy}{dx} = \frac{x^3}{y}\) - **D.** \(\frac{dy}{dx} = \frac{x^2}{y^2}\) (NOTE: Option **C** has been marked as the correct answer.) #### Explanation of the Slope Field Graph The graph on the right is a slope field (or direction field) that visually represents the slopes of a differential equation at various points \((x, y)\) on the plane. Each small segment or line in the field indicates the slope of the solution curve at that specific point. The slope field provides an intuitive way to see the behavior of solutions to differential equations without solving the equation analytically. The horizontal axis represents the \(x\)-coordinate, and the vertical axis represents the \(y\)-coordinate. **Key Features to Note:** 1. The slope lines vary in direction and steepness across different points. 2. As \(x\) and \(y\) values change, the slope of the lines adjusts accordingly, representing the differential equation's behavior. This specific slope field corresponds to the differential equation \(\frac{dy}{dx} = \frac{x^3}{y}\). This is validated by observing the pattern of the lines' slopes and matching it with the given options.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS