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...
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Topic: Exact DE
please answer number 23
![15. (sin
2r cos²0) dr + r cos 0(2r sin 0 + 1) d0 = 0.
16. [2x + y cos (xy)] dx + x cos (xy) dy = 0.
17. 2xy dx + (y² + x²) dy = 0.
18. 2xy dx + (y² – x²) dy = 0.
19. |2xy cos (x²) — 2xy + 1] dx + [sin (x²) — x²] dy = 0.
ANS.
20. (2x - 3y) dx + (2y − 3x) dy = 0.
21. Do exercise 20 by a second method.
22. (xy² + y − x) dx + x(xy + 1) dy = 0.
23. 3y(x² − 1) dx + (x³ + 8y − 3x) dy = 0; when x
ANS. r sin 0 r² cos² 0 = c.
ANS. x² + sin (xy) = C.
ANS. y(3x² + y²)
= C.
ANS. x² + y² = cy.
=
-
y[sin (x²) — x²] = =C-X.
ANS. x² + y² - 3xy =
= C.
ANS. x²y² + 2xy − x² = c
: 0, y = 1.
ANS.
xy(x² − 3) = 4(1 − y²).
_ |||
O](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd71a618d-9836-464b-8c0a-0a2658aa9dd0%2F2440914e-2375-4b52-8794-9382b29919a9%2Fohzfhur_processed.jpeg&w=3840&q=75)
Transcribed Image Text:15. (sin
2r cos²0) dr + r cos 0(2r sin 0 + 1) d0 = 0.
16. [2x + y cos (xy)] dx + x cos (xy) dy = 0.
17. 2xy dx + (y² + x²) dy = 0.
18. 2xy dx + (y² – x²) dy = 0.
19. |2xy cos (x²) — 2xy + 1] dx + [sin (x²) — x²] dy = 0.
ANS.
20. (2x - 3y) dx + (2y − 3x) dy = 0.
21. Do exercise 20 by a second method.
22. (xy² + y − x) dx + x(xy + 1) dy = 0.
23. 3y(x² − 1) dx + (x³ + 8y − 3x) dy = 0; when x
ANS. r sin 0 r² cos² 0 = c.
ANS. x² + sin (xy) = C.
ANS. y(3x² + y²)
= C.
ANS. x² + y² = cy.
=
-
y[sin (x²) — x²] = =C-X.
ANS. x² + y² - 3xy =
= C.
ANS. x²y² + 2xy − x² = c
: 0, y = 1.
ANS.
xy(x² − 3) = 4(1 − y²).
_ |||
O
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