Please answer numbers 3,7,9,11, 15,19 and 28 TNT4G+al ll20% I1 4:38GLOBEEdit50Exact Method ExercisesExercisesTest cach of the following equations for exactness and solve the eqcation. The equa-tions that are not exact may be solved by methods discussed in he precedingsections.+ 2x, -L (x+ y) dx +(x- y) dy 02. (6x+y) dx + y(2x-3y) dy 0,3. (2xy-3xty dx + (x+ y) dy-0.4. (y - 2xy+ 6x) dx- (x-2xy ++ 2) dy = 0.(2xy + y) dx 4 (x(x- 2y) dx + 2y -x) dy-0.Ans.Ans. 3x + xy²Ans. xy-y=c.Ans. xy+3x22y =c.y= ex(x- 1)-34xy +c.x)dy-0.Ans.Ans.x²+2y²37Sec. 11]The Linear Equntion of Order One7. Do Exercise 6 by another method.&. (2x-3y) dx+(2y-3x) dy -0.9. Do Exercise 8 by another method.10. (2u-3) du + (3u u- 3u + 40) de 0.1. (cos 2y-3xy) dx + (cos 2y-2x sin 2y- 2x'y) dy 0.Ans. x + y == 3xy + c.Ans. (u*p² - 3u + 2v) = c.12. (1 + y) dx (xy + y) dy -0.13. (1+y+ xy) dx + (xy + y + 2xy) dy=0.• 14. (w+wz-z) dw + (z³ + w²z - w) dz -0.15. (2xy-tan y) dx + (xAns. sin 2y + x cos 2y-x'y² = c.Ans. 2 arc tan x+ In (1 + y) =e.Ans. 2x +y(1 + x}² = e.Ans. (w + z) = 4wz + c.Ans. xy-x tan y e.• 16. (cos x cos y- cot x) dx - sin x sin y dy-0. Ans. sin x cos y= In |c sin x|.

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Description: Please answer numbers 3,7,9,11, 15,19 and 28 TNT4G+al ll20% I1 4:38GLOBEEdit50Exact Method ExercisesExercisesTest cach of the following equations for exactness and solve the eqcation. The equa-tions that are not exact may be solved by methods discuss

We consider here the following standard form of ordinary differential equation. M(x,y)dx…

Answered: 3. (2xy-3xty dx + (x + y) dy

Math

Calculus

3. (2xy-3xty dx + (x + y) dy

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 Video

Question

Please answer numbers 3,7,9,11, 15,19 and 28

TNT
4G+
al ll
20% I1 4:38
GLOBE
Edit
50
Exact Method Exercises
Exercises
Test cach of the following equations for exactness and solve the eqcation. The equa-
tions that are not exact may be solved by methods discussed in he preceding
sections.
+ 2x, -
L (x+ y) dx +(x- y) dy 0
2. (6x+y) dx + y(2x-3y) dy 0,
3. (2xy-3xty dx + (x+ y) dy-0.
4. (y - 2xy+ 6x) dx- (x-2xy ++ 2) dy = 0.
(2xy + y) dx 4 (x
(x- 2y) dx + 2y -x) dy-0.
Ans.
Ans. 3x + xy²
Ans. xy
-y=c.
Ans. xy
+3x2
2y =c.
y= ex(x- 1)-3
4xy +c.
x)dy-0.
Ans.
Ans.
x²+2y²
37
Sec. 11]
The Linear Equntion of Order One
7. Do Exercise 6 by another method.
&. (2x-3y) dx+(2y-3x) dy -0.
9. Do Exercise 8 by another method.
10. (2u-3) du + (3u u- 3u + 40) de 0.
1. (cos 2y-3xy) dx + (cos 2y-2x sin 2y- 2x'y) dy 0.
Ans. x + y == 3xy + c.
Ans. (u*p² - 3u + 2v) = c.
12. (1 + y) dx (xy + y) dy -0.
13. (1+y+ xy) dx + (xy + y + 2xy) dy=0.
• 14. (w+wz-z) dw + (z³ + w²z - w) dz -0.
15. (2xy-tan y) dx + (x
Ans. sin 2y + x cos 2y-x'y² = c.
Ans. 2 arc tan x+ In (1 + y) =e.
Ans. 2x +y(1 + x}² = e.
Ans. (w + z) = 4wz + c.
Ans. xy-x tan y e.
• 16. (cos x cos y- cot x) dx - sin x sin y dy-0. Ans. sin x cos y= In |c sin x|.
<x sec y) dy =0
• 17. (r + sin 6- cos 6) dr + r(sin 0+ cos 0) de-0.
Ans. + 2r{sin @- cos 0) c.
V 18. x(3xy
4y+ 6) dx + (x-6x'y-1) dy 0.
Ans. xy-2x²y? + 3x² - y =c.
wr19. (sin e-2r cos dr +r cos 0(2r sin e + 1) de = 0.
Ans.
20. [2x + y cos (xy)] dx + x cos (xy) dy = 0.
21. 2xy dx + (y² + x*) dy 0.
• 22. 2xy dx +(G²-x) dy = 0.
. 23. (xy +y – x) dx + x(xy + 1) dy-0.
, 24. 3y(x-
r sin - cos =e.
Ans. x+sin (xy) = c.
Ans. (3x +y)-c.
Ans. x+y= cy.
Ans. xy +2xy-x c.
1) dx + (x + 8y-3x) dy = 0; when x 0, y -1.
Ans. xy(x-3)= 4(1- y)
25. (1-xy) dx + [y +x*(1-xy)] dy = 0; when x = 2, y L.
Ans. xy-y +5xy-3x 5.
(3+y+2y² sin? x) dx + (x + 2xy- y sin 2x) dy 0.
Ans. y sin 2x e+2x(3+y + y)
27. 2x[3x + y-y exp (-x)] dx + [x + 3y +exp (-x)] dy-0.
Aus. xy+ y+ 2x + y exp (-x)-c.
28. (xy+x-2y +3) dx + x²y dy 2(x+ y) dy; when x 1, y = 1.
Ans. (xy-2) + (x+3) 2y + 15.
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