8:36 Aa 4» Q A ceed as in Example 6, by considering ø simply as a function and give its domain. Then by considering o as a solution of the differential equation, give at least one interval I of definition. 15. (у — х)у' —у — х+ 8; у%3Dх + 4Vx+ 2 16. y' = 25 + y²; y= 5 tan 5x In 17. y' = 2xy²; y = 1/(4 – x²) SC - 1/2 18. 2y' — уз сos x; у%3D (1 — sin x) 3 In Problems 19 and 20 verify that the indicated expression is an im- plicit solution of the given first-order differential equation. Find at least one explicit solution y = p(x) in each case. Use a graphing util- ity to obtain the graph of an explicit solution. Give an interval I of definition of each solution p. In 3 2X – 1 dX 19. dt (X – 1)(1 2X); In In 20. 2xy dx + (x2² – y) dy = 0; –2x²y + y² = 1 co di In Problems 21–24 verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. 3 In dP 21. dt Ce' P(1 - P); 1 + cje' SC (- dy 22. - + 4xy dx 8x; y = 2x² – 1 + cje -212 4 d?y dy 4 + 4y = 0; y = cje2x + c2xe2x 23. dx2 dx * 2r2d?, dx? d³y dy 12x2; 24. dx3 + y х dx 1 y = c1x + С2х + Сэх In x + 4x2 In Problems 25–28 use (12) to verify that the indicated function is 4 13 Reader Notebook Bookmarks Flashcards Contents IK ШО
8:36 Aa 4» Q A ceed as in Example 6, by considering ø simply as a function and give its domain. Then by considering o as a solution of the differential equation, give at least one interval I of definition. 15. (у — х)у' —у — х+ 8; у%3Dх + 4Vx+ 2 16. y' = 25 + y²; y= 5 tan 5x In 17. y' = 2xy²; y = 1/(4 – x²) SC - 1/2 18. 2y' — уз сos x; у%3D (1 — sin x) 3 In Problems 19 and 20 verify that the indicated expression is an im- plicit solution of the given first-order differential equation. Find at least one explicit solution y = p(x) in each case. Use a graphing util- ity to obtain the graph of an explicit solution. Give an interval I of definition of each solution p. In 3 2X – 1 dX 19. dt (X – 1)(1 2X); In In 20. 2xy dx + (x2² – y) dy = 0; –2x²y + y² = 1 co di In Problems 21–24 verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. 3 In dP 21. dt Ce' P(1 - P); 1 + cje' SC (- dy 22. - + 4xy dx 8x; y = 2x² – 1 + cje -212 4 d?y dy 4 + 4y = 0; y = cje2x + c2xe2x 23. dx2 dx * 2r2d?, dx? d³y dy 12x2; 24. dx3 + y х dx 1 y = c1x + С2х + Сэх In x + 4x2 In Problems 25–28 use (12) to verify that the indicated function is 4 13 Reader Notebook Bookmarks Flashcards Contents IK ШО
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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Transcribed Image Text:8:36
Aa 4» Q A
ceed as in Example 6, by considering ø simply as a function and give
its domain. Then by considering o as a solution of the differential
equation, give at least one interval I of definition.
15. (у — х)у' —у — х+ 8; у%3Dх + 4Vx+ 2
16. y' = 25 + y²; y= 5 tan 5x
In
17. y' = 2xy²; y = 1/(4 – x²)
SC
- 1/2
18. 2y' — уз сos x; у%3D (1 — sin x)
3
In Problems 19 and 20 verify that the indicated expression is an im-
plicit solution of the given first-order differential equation. Find at
least one explicit solution y = p(x) in each case. Use a graphing util-
ity to obtain the graph of an explicit solution. Give an interval I of
definition of each solution p.
In
3
2X – 1
dX
19.
dt
(X – 1)(1
2X); In
In
20. 2xy dx + (x2² – y) dy = 0; –2x²y + y² = 1
co
di
In Problems 21–24 verify that the indicated family of functions is a
solution of the given differential equation. Assume an appropriate
interval I of definition for each solution.
3
In
dP
21.
dt
Ce'
P(1
- P);
1 + cje'
SC
(-
dy
22. - + 4xy
dx
8x; y =
2x² – 1 + cje
-212
4
d?y
dy
4
+ 4y = 0; y = cje2x + c2xe2x
23.
dx2
dx
* 2r2d?,
dx?
d³y
dy
12x2;
24.
dx3
+ y
х
dx
1
y = c1x
+ С2х + Сэх In x + 4x2
In Problems 25–28 use (12) to verify that the indicated function is
4
13
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