Homework Help is Here – Start Your Trial Now!
Math
Calculus
dy Solve the initial-value problem for y as a function of x. (16-2²) d = 1, y(0) = 9 y +9 X

dy Solve the initial-value problem for y as a function of x. (16-2²) d = 1, y(0) = 9 y +9 X

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
Solve the initial-value problem for \( y \) as a function of \( x \). \[ (16 - x^2) \frac{dy}{dx} = 1, \quad y(0) = 9 \] The solution for \( y \) is given by: \[ y = \frac{1}{4} \ln \left| \frac{x+4}{x-4} \right| + 9 \]
Transcribed Image Text:Solve the initial-value problem for \( y \) as a function of \( x \). \[ (16 - x^2) \frac{dy}{dx} = 1, \quad y(0) = 9 \] The solution for \( y \) is given by: \[ y = \frac{1}{4} \ln \left| \frac{x+4}{x-4} \right| + 9 \]
Expert Solution
Step 1: Given:

The given initial value problem is:

open parentheses 16 minus straight x squared close parentheses dy over dx equals 1 comma space space space space space space straight y left parenthesis 0 right parenthesis equals 9

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