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3u + 4v) dv 6. v(2up - 3) du + (3u²u 7. (cos 2y = 3x²y²) dx + (cos 2y – 2x sin 2y – 2x³y) dy = 0. + ne ANS. sin 2y + x cos 2y – x'y² C. ANS. 2 arc tan x+ In (1 + y²) = c. 8. (1 + y²) dx + (x²y + y) dy = 0.

3u + 4v) dv 6. v(2up - 3) du + (3u²u 7. (cos 2y = 3x²y²) dx + (cos 2y – 2x sin 2y – 2x³y) dy = 0. + ne ANS. sin 2y + x cos 2y – x'y² C. ANS. 2 arc tan x+ In (1 + y²) = c. 8. (1 + y²) dx + (x²y + y) dy = 0.

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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6-10) 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.
6. v(2uD - 3) du + (3u²v² 1. (cos 2y 3x²y²) dx + (cos 2y – 2x sin 2y – 2x'y) dy = 0. 3u + 4v) dv = 8. (1 + y') dx + (x²y + y) dy = 0. 9. (1 + y² + xy°) dx + (x²y + y + 2xy) dy = 0. 10. (w3 + wz2 - 2) dw + (z² + w²z - w) dz = 0. 11. (2xy = tan y) dx + (x² ANS. sin 2y + x cos 2y – x'y C. 2 arc tan x + In (1 + y') = c. ANS. 2x + y (1+ x)² = c. ANS. (w2 +z²)² = 4wz + c. ANS. x²y - x tan y = c. ANS. x sec? y) dy = 0.
Transcribed Image Text:6. v(2uD - 3) du + (3u²v² 1. (cos 2y 3x²y²) dx + (cos 2y – 2x sin 2y – 2x'y) dy = 0. 3u + 4v) dv = 8. (1 + y') dx + (x²y + y) dy = 0. 9. (1 + y² + xy°) dx + (x²y + y + 2xy) dy = 0. 10. (w3 + wz2 - 2) dw + (z² + w²z - w) dz = 0. 11. (2xy = tan y) dx + (x² ANS. sin 2y + x cos 2y – x'y C. 2 arc tan x + In (1 + y') = c. ANS. 2x + y (1+ x)² = c. ANS. (w2 +z²)² = 4wz + c. ANS. x²y - x tan y = c. ANS. x sec? y) dy = 0.
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