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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Question
Please answer number 16
![11. x² dx + y(x - 1) dy = 0.
12. (xy + x) dx = (x²y² + x² + y² + 1) dy.
ANS.
13. x cos2 y dx + tan y dy = 0.
-x
14. xy³ dx + (y + 1) e¯* dy = 0.
15. x²yy' = e".
16. tan² y dy = sin³ x dx.
17. y' = cos2x cos y.
18. y' = y sec x.
19. dx =
t(1 + t²) sec² x dt.
20. (e²x + 4)y' = y.
21. a dB + Bda + aB(3 da + dB) = 0.
22. (1+ ln x) dx + (1 + ln y) dy = 0.
x² dy
23. x dx
a²
= 0.
ANS. (x + 1)² + y² + 2 ln [c(x − 1)] = 0.
In (x² + 1) = y² – 2y + 4 ln [c(y + 1)].
ANS. x² + tan² y = c².
ANS.
ANS.
ANS. e*(x - 1)
1 1
ANS.
= +
y
ANS. x(y + 1) = (1
cos³ x - 3 cos x = 3(tan y
4 ln |sec y + tan yl =
2y²
+ c.
+ cx) e³.
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).
ANS. x ln x + y ln y = c.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd71a618d-9836-464b-8c0a-0a2658aa9dd0%2F731573cc-3d21-45d8-a48b-7869ccfc5af3%2Fu73q36ki_processed.jpeg&w=3840&q=75)
Transcribed Image Text:11. x² dx + y(x - 1) dy = 0.
12. (xy + x) dx = (x²y² + x² + y² + 1) dy.
ANS.
13. x cos2 y dx + tan y dy = 0.
-x
14. xy³ dx + (y + 1) e¯* dy = 0.
15. x²yy' = e".
16. tan² y dy = sin³ x dx.
17. y' = cos2x cos y.
18. y' = y sec x.
19. dx =
t(1 + t²) sec² x dt.
20. (e²x + 4)y' = y.
21. a dB + Bda + aB(3 da + dB) = 0.
22. (1+ ln x) dx + (1 + ln y) dy = 0.
x² dy
23. x dx
a²
= 0.
ANS. (x + 1)² + y² + 2 ln [c(x − 1)] = 0.
In (x² + 1) = y² – 2y + 4 ln [c(y + 1)].
ANS. x² + tan² y = c².
ANS.
ANS.
ANS. e*(x - 1)
1 1
ANS.
= +
y
ANS. x(y + 1) = (1
cos³ x - 3 cos x = 3(tan y
4 ln |sec y + tan yl =
2y²
+ c.
+ cx) e³.
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).
ANS. x ln x + y ln y = c.
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