Solve the differential equation [x a. b. C. d. y tan ¹()] 2x tan-¹(²) -¹ (²/2) dx + x tan¯¹ (²/2)dy = 0 |c²(x² + y²) 24 2y tan-¹(²) = x ln -1 2x tan-¹ () = x ln x In c² (x² + y²) y4 | c² (x² + y²) 2y tan-¹() = x ln c² (x²+y²) |

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

Using Homogenous Differential Equation

Solve the differential equation
[x
-
a.
b.
C.
d.
-1
y tan-¹ (2)] dx + x tan
= x In |
| c² (x² + y²)
x4
-1
2x tan-¹(²):
-1
2x tan-¹ (/) = x ln
2y
tan-¹ (/) = x ln
2ytan ¹ (2) = x ln
| c² (x² + y²)
y4
| c² (x² + y²)
y4
c²2(x² + y²)
x4
(2/2) dy=0
Transcribed Image Text:Solve the differential equation [x - a. b. C. d. -1 y tan-¹ (2)] dx + x tan = x In | | c² (x² + y²) x4 -1 2x tan-¹(²): -1 2x tan-¹ (/) = x ln 2y tan-¹ (/) = x ln 2ytan ¹ (2) = x ln | c² (x² + y²) y4 | c² (x² + y²) y4 c²2(x² + y²) x4 (2/2) dy=0
Expert Solution
steps

Step by step

Solved in 3 steps with 6 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