+ + 22. (1+ ln x) dx + (1 + ln y) dy = 0. 23. xdx −/ ² ・x² dy = 0₁ P). ANS. x ln x + y ln y = c. ANS.

Calculus: Early Transcendentals
8th Edition
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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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Please solve number 22
14. xy³ dx + (y + 1) e¯* dy = 0.
15. x²yy' = e'.
16. tan² y dy = sin³ x dx.
cos² x cos y.
17. y'
18. y' =
19. dx
20. (e²x + 4)y' = y.
21. a dß + ß da + αß(3 da + dß) = 0.
22. (1+ ln x) dx + (1 + ln y) dy = 0.
=
=
y sec x.
t(1 + t²) sec² x dt.
23. xdx − vả − x dy = 0.
-
ANS. y-c=-
24. x dx +
a² — x² dy = 0.
ANS. y − c =
ANS._ e*(x − 1) = − +
y 2y²
ANS. x(y + 1) = (1
ANS. COS³ x
3 cos x =
ANS. 4 ln |sec y + tan yl
ANS.
+ c.
+ cx) e³.
3(tan y y + c).
= 2x + sin 2x + c.
ANS. y = c(sec x + tan x).
2x + sin 2x = c + (1 + t²)².
ANS. y³(1 + 4e¯²x) = c².
ANS. caß = exp(-3x - ß).
x ln x + y ln y = c.
ANS.
a²-x², the lower half of the circle x² + (y − c)² = a².
a²-x², the upper half of the circle x² + (y − c)² = a².
y + c
Transcribed Image Text:14. xy³ dx + (y + 1) e¯* dy = 0. 15. x²yy' = e'. 16. tan² y dy = sin³ x dx. cos² x cos y. 17. y' 18. y' = 19. dx 20. (e²x + 4)y' = y. 21. a dß + ß da + αß(3 da + dß) = 0. 22. (1+ ln x) dx + (1 + ln y) dy = 0. = = y sec x. t(1 + t²) sec² x dt. 23. xdx − vả − x dy = 0. - ANS. y-c=- 24. x dx + a² — x² dy = 0. ANS. y − c = ANS._ e*(x − 1) = − + y 2y² ANS. x(y + 1) = (1 ANS. COS³ x 3 cos x = ANS. 4 ln |sec y + tan yl ANS. + c. + cx) e³. 3(tan y y + c). = 2x + sin 2x + c. ANS. y = c(sec x + tan x). 2x + sin 2x = c + (1 + t²)². ANS. y³(1 + 4e¯²x) = c². ANS. caß = exp(-3x - ß). x ln x + y ln y = c. ANS. a²-x², the lower half of the circle x² + (y − c)² = a². a²-x², the upper half of the circle x² + (y − c)² = a². y + c
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