Verify that the indicated function y = (x) is an explicit solution of the given first-order differential equation. y' = 2xy2; y = 1/(9-x²) When y = 1/(9-x²), y' = Thus, in terms of x, 2xy² = Since the left and right hand sides of the differential equation are equal when 1/(9-x2) is substituted for y, y = 1/(9-x2) is a solution. Proceed as in Example 6, by considering o simply as a function and give its domain. (Enter your answer using interval notation.) Then by considering as a solution of the differential equation, give at least one interval I of definition. O (-00, 0) [3,00) O (0,00) O (-3, 3)

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...
icon
Related questions
Question
Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation.
y' = 2xy²; y = 1/(9-x²)
When y = 1/(9-x²),
y' =
Thus, in terms of x,
2xy²
Since the left and right hand sides of the differential equation are equal when 1/(9-x2) is substituted for y, y = 1/(9-x²) is a solution.
Proceed as in Example 6, by considering simply as a function and give its domain. (Enter your answer using interval notation.)
Then by considering as a solution of the differential equation, give at least one interval I of definition.
O (-00, 0)
O [3,00)
O (0,00)
O (-3, 3)
O (-00, -3]
Transcribed Image Text:Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation. y' = 2xy²; y = 1/(9-x²) When y = 1/(9-x²), y' = Thus, in terms of x, 2xy² Since the left and right hand sides of the differential equation are equal when 1/(9-x2) is substituted for y, y = 1/(9-x²) is a solution. Proceed as in Example 6, by considering simply as a function and give its domain. (Enter your answer using interval notation.) Then by considering as a solution of the differential equation, give at least one interval I of definition. O (-00, 0) O [3,00) O (0,00) O (-3, 3) O (-00, -3]
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

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