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...
Related questions
Question
Topic: homogeneous DE,
Please answer number 25
![23. (x - y) dx + (3x + y) dy = 0; when x = 2, y = -1.
ANS. _2(x + 2y) + (x + y) ln (x + y) = 0.
ANS. x² = 9 6y.
ANS. x² = 2y + 1.
tan (y/x) = ln (e/x).
x - y = 5(y + 4x) ln x.
4(2y + x) ln y = 2y - - X.
ANS. y(3x² + 4y²) = 4.
29. xy dx + 2(x² + 2y²) dy = 0; when x = 0, y = 1.
30. y(2x² - xy + y²) dx − x²(2x − y) dy = 0; when x = 1, y = 1.
ANS. y2 In x = 2y² + xy − x².
31. y(9x2y) dx − x(6x − y) dy = 0; when x = 1, y = 1.
3x³x²y - 2y² = 0.
V
24. (y
25. (y +
/x² + y²) dx − x dy = 0; when x = √√3, y = 1.
/x² + y²) dx − x dy = 0; when x = √√√3, y = 1.
V
=
26. [x cos² (y/x) − y] dx + x dy = 0; when x
1, y = π/4.
27. (y² + 7xy + 16x²) dx + x² dy
=
0; when x =
= 1, y = 1.
ANS.
28. y² dx + (x² + 3xy + 4y²) dy = 0; when x = 2, y = 1.
ANS.
ANS.
ANS.
32. y(x² + y²) dx + x(3x² − 5y²) dy = 0; when x = 2, y = 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd71a618d-9836-464b-8c0a-0a2658aa9dd0%2F10ca5690-4d2e-4cc1-a8e4-211b95af6899%2F2wbnfkm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:23. (x - y) dx + (3x + y) dy = 0; when x = 2, y = -1.
ANS. _2(x + 2y) + (x + y) ln (x + y) = 0.
ANS. x² = 9 6y.
ANS. x² = 2y + 1.
tan (y/x) = ln (e/x).
x - y = 5(y + 4x) ln x.
4(2y + x) ln y = 2y - - X.
ANS. y(3x² + 4y²) = 4.
29. xy dx + 2(x² + 2y²) dy = 0; when x = 0, y = 1.
30. y(2x² - xy + y²) dx − x²(2x − y) dy = 0; when x = 1, y = 1.
ANS. y2 In x = 2y² + xy − x².
31. y(9x2y) dx − x(6x − y) dy = 0; when x = 1, y = 1.
3x³x²y - 2y² = 0.
V
24. (y
25. (y +
/x² + y²) dx − x dy = 0; when x = √√3, y = 1.
/x² + y²) dx − x dy = 0; when x = √√√3, y = 1.
V
=
26. [x cos² (y/x) − y] dx + x dy = 0; when x
1, y = π/4.
27. (y² + 7xy + 16x²) dx + x² dy
=
0; when x =
= 1, y = 1.
ANS.
28. y² dx + (x² + 3xy + 4y²) dy = 0; when x = 2, y = 1.
ANS.
ANS.
ANS.
32. y(x² + y²) dx + x(3x² − 5y²) dy = 0; when x = 2, y = 1.
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