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1 2 + y? + 1) dx + x(x-2y) dy = 0. %3D

1 2 + y? + 1) dx + x(x-2y) dy = 0. %3D

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter13: Conic Sections
Section13.1: Circles
Problem 48PS
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use determination of integrating factors

functions of the same degree, and if Mx + Ny #0, then Use Euler's theorem to prove the result that, if M and N an Solve each of the following equations. Exercises 1. (x2 + y+ 1) dx + x(x- 2y) dy 0. 2. 2yx? - y + x) dx + (x² – 2y) dy = 0. 3. y(2x - y+ 1) dx + x(3x-4y + 3) dy = 0. 4. y(4x + y) dx - 2(x² – y) dy =0. 5. (xy+ 1) dx + x(x +4y- 2) dy = 0, 6. (2y + 3xy- 2p + 6x) dx + x(x+ 2y- 1) dy = 0. Ans. Ans. Ans. xy Ans. 2x +xy Ans. xy + In x Ans. x(y +. 1. yly + 2x – 2) dx - 2(x + y) dy = 0. &. y dx + (3xy + y? - 1) dy = 0. 9. 2y(x + y + 2) dx + (y² – x² – 4x - 1) dy = 0. Ans. Ans. y (y Ans. x + 2xy+y 10. 2(2y + 5xy - 2y + 4) dx + x(2x + 2y- 1) dy = 0. Ans. x(y+2 Ans. x(x 11. 3(x2 + y?) dx + x(x? + 3y² + 6y) dy = 0. 12 8x-9y) dx + 2x(x - 3y) dy = 0. 13. Do Exercise 12 by another method. . y(2x2 - xy + 1) dx + (x- y) dy = 0. 5. Euler's theorem (Exercise 36, page 32) on homogeneous functic * Is a homogeneous function of degree k in x and y, then Ans. %3D Ans. y(2x-) OF OF + y dy. %3D dx Mx + Ny
Transcribed Image Text:functions of the same degree, and if Mx + Ny #0, then Use Euler's theorem to prove the result that, if M and N an Solve each of the following equations. Exercises 1. (x2 + y+ 1) dx + x(x- 2y) dy 0. 2. 2yx? - y + x) dx + (x² – 2y) dy = 0. 3. y(2x - y+ 1) dx + x(3x-4y + 3) dy = 0. 4. y(4x + y) dx - 2(x² – y) dy =0. 5. (xy+ 1) dx + x(x +4y- 2) dy = 0, 6. (2y + 3xy- 2p + 6x) dx + x(x+ 2y- 1) dy = 0. Ans. Ans. Ans. xy Ans. 2x +xy Ans. xy + In x Ans. x(y +. 1. yly + 2x – 2) dx - 2(x + y) dy = 0. &. y dx + (3xy + y? - 1) dy = 0. 9. 2y(x + y + 2) dx + (y² – x² – 4x - 1) dy = 0. Ans. Ans. y (y Ans. x + 2xy+y 10. 2(2y + 5xy - 2y + 4) dx + x(2x + 2y- 1) dy = 0. Ans. x(y+2 Ans. x(x 11. 3(x2 + y?) dx + x(x? + 3y² + 6y) dy = 0. 12 8x-9y) dx + 2x(x - 3y) dy = 0. 13. Do Exercise 12 by another method. . y(2x2 - xy + 1) dx + (x- y) dy = 0. 5. Euler's theorem (Exercise 36, page 32) on homogeneous functic * Is a homogeneous function of degree k in x and y, then Ans. %3D Ans. y(2x-) OF OF + y dy. %3D dx Mx + Ny
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