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.
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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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