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11. (2xy - tan y) dx + (x - x sec y) dy = 0. ANS. Xy - x tan y = c.

11. (2xy - tan y) dx + (x - x sec y) dy = 0. ANS. Xy - x tan y = c.

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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11-15) Test each of the following equations for exactness and solve the equation. The equations that are not exact may be solved by other methods. Show complete solution.
11. (2xy – tan y) dx + (x 12. (cos x cos y 13. (+ sin 8 x sec? y) dy = 0. sin x sin y dy = 0. ANS, X'y - x tan y = c. sin x cos y %3D In c sin xl. cot x) dx - - cos 0) dr + r(sin 0 + cos 0) d0 = 0. ANS. ANS. r2 + 2r(sin 0 – cos 0) = C. 14. x(3xy-4y + 6) dx + (x² – 6x²y? – 1) dy = 0. ANS. x'y- 2x²y³ + 3x² – y = c. 15. (sin 6 2r cos? 0) dr + r cos 6(2r sin 0 + 1) d0 = 0. ANS. r sin 0 = cos2 0 = c.
Transcribed Image Text:11. (2xy – tan y) dx + (x 12. (cos x cos y 13. (+ sin 8 x sec? y) dy = 0. sin x sin y dy = 0. ANS, X'y - x tan y = c. sin x cos y %3D In c sin xl. cot x) dx - - cos 0) dr + r(sin 0 + cos 0) d0 = 0. ANS. ANS. r2 + 2r(sin 0 – cos 0) = C. 14. x(3xy-4y + 6) dx + (x² – 6x²y? – 1) dy = 0. ANS. x'y- 2x²y³ + 3x² – y = c. 15. (sin 6 2r cos? 0) dr + r cos 6(2r sin 0 + 1) d0 = 0. ANS. r sin 0 = cos2 0 = c.
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