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6. 2 dx + (2x - y + 3) dy = 0. Use a change of variable. ANS. y + c = −ln |2x − y + 4). 7. Solve the equation of exercise 6 by using the fact that the equation is linear in x. 8. (xy + 2) dx + 3 dy = 0. ANS. x + c = 3 ln |x − y + 5. 9. Solve exercise 8 by another method. 10. (x + y − 1) dx + (2x + 2y + 1) dy = 0. ANS. x + 2y + c = 3 ln x + y + 21.

6. 2 dx + (2x - y + 3) dy = 0. Use a change of variable. ANS. y + c = −ln |2x − y + 4). 7. Solve the equation of exercise 6 by using the fact that the equation is linear in x. 8. (xy + 2) dx + 3 dy = 0. ANS. x + c = 3 ln |x − y + 5. 9. Solve exercise 8 by another method. 10. (x + y − 1) dx + (2x + 2y + 1) dy = 0. ANS. x + 2y + c = 3 ln x + y + 21.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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" Coefficients linear in the two variables " ASAP. Thank you

6. 2 dx + (2x - y + 3) dy = 0. Use a change of variable. ANS. y + c = −ln |2x − y + 4). 7. Solve the equation of exercise 6 by using the fact that the equation is linear in x. 8. (xy + 2) dx + 3 dy = 0. ANS. x + c = 3 ln |x − y + 5. 9. Solve exercise 8 by another method. 10. (x + y − 1) dx + (2x + 2y + 1) dy = 0. ANS. x + 2y + c = 3 ln x + y + 21.
Transcribed Image Text:6. 2 dx + (2x - y + 3) dy = 0. Use a change of variable. ANS. y + c = −ln |2x − y + 4). 7. Solve the equation of exercise 6 by using the fact that the equation is linear in x. 8. (xy + 2) dx + 3 dy = 0. ANS. x + c = 3 ln |x − y + 5. 9. Solve exercise 8 by another method. 10. (x + y − 1) dx + (2x + 2y + 1) dy = 0. ANS. x + 2y + c = 3 ln x + y + 21.
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