Homework Help is Here – Start Your Trial Now!
Math
Calculus
Verify that the given differential equation is not exact. (-xy sin(x) + 2y cos(x)) dx + 2x cos(x) dy = 0 If the given DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has -x sin(x) + 2 cos(x) My Solve. Nx = = Since My and Nx are not ♦ equal, the equation is not exact. Multiply the given differential equation by the integrating factor μ(x, y) = xy and verify that the new equation is exact. If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has Nx My -x²y²sin(x) + 2xy²cos(x) x = Since My 2 cos(x) - 2x sin(x) = and N 2x²y sin(x) x X are equal, the equation is exact. -x²cos(x) + 2(x sin(x) + cos(x)) ×

Verify that the given differential equation is not exact. (-xy sin(x) + 2y cos(x)) dx + 2x cos(x) dy = 0 If the given DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has -x sin(x) + 2 cos(x) My Solve. Nx = = Since My and Nx are not ♦ equal, the equation is not exact. Multiply the given differential equation by the integrating factor μ(x, y) = xy and verify that the new equation is exact. If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has Nx My -x²y²sin(x) + 2xy²cos(x) x = Since My 2 cos(x) - 2x sin(x) = and N 2x²y sin(x) x X are equal, the equation is exact. -x²cos(x) + 2(x sin(x) + cos(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
Verify that the given differential equation is not exact. (-xy sin(x) + 2y cos(x)) dx + 2x cos(x) dy = 0 If the given DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has -x sin(x) + 2 cos(x) My Solve. Nx N = Since M₁, and N. My equal, the equation is not exact. X Multiply the given differential equation by the integrating factor µ(x, y) = xy and verify that the new equation is exact. If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has My = -x²2y²sin(x) + 2xy²cos(x) x X = 2 cos(x) - 2x sin(x) = are not 2x²y sin(x) x Since My and Nare ♦ equal, the equation is exact. -x²cos(x) + 2(xsin(x) + cos(x)) x
Transcribed Image Text:Verify that the given differential equation is not exact. (-xy sin(x) + 2y cos(x)) dx + 2x cos(x) dy = 0 If the given DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has -x sin(x) + 2 cos(x) My Solve. Nx N = Since M₁, and N. My equal, the equation is not exact. X Multiply the given differential equation by the integrating factor µ(x, y) = xy and verify that the new equation is exact. If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has My = -x²2y²sin(x) + 2xy²cos(x) x X = 2 cos(x) - 2x sin(x) = are not 2x²y sin(x) x Since My and Nare ♦ equal, the equation is exact. -x²cos(x) + 2(xsin(x) + cos(x)) x
Expert Solution
steps

Step by step

Solved in 2 steps with 2 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