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19. |2xy cos (x²) − 2xy + 1] dx + [sin (x²) − x²] dy = 0. ANS. y[sin (x²) x²] = c - x.

19. |2xy cos (x²) − 2xy + 1] dx + [sin (x²) − x²] dy = 0. ANS. y[sin (x²) x²] = c - 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...
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Topic: Exact DE please answer number 19
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
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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