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(1 – xy)-2 dx + [y² + x²(1 – xy)-2] dy = 0; when x = 4, y = 1.

(1 – xy)-2 dx + [y² + x²(1 – xy)-2] dy = 0; when x = 4, y = 1.

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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36 Equations of Order One [Ch. 2 - 2 24. (1 – xy)-2 dx + [y² + x²(1 – xy)-²] dy = 0; when x = 4, y = 1. ANS. хy* — уз + 3ху — 3х — 3 %3D 0. - 25. (ye* – 2y³) dx + (x e*" – 6xy² – 2y) dy = 0; when x = 0, y = 2. ANS. e*y = 2xy³ + y² – 3. = 0. = c + 2x(3 + y + y²). 26. (3 + y + 2y² sin² x) dx + (x + 2xy – y sin 2x) dy ANS. y? sin 2x 27. 2x[3x + у — у ехр (— х?)] dx + [x? + 3у? + еxp (-х?) dy 3D 0. ANS. x²y + y³ + 2x³ + y exp (–-x²) = c. | 28. (ху? + х — 2у + 3) dx + x^у dy 3D 2(х + у) dy; when x 3D 1, у %3D 1. ANS. (xy – 2)2 + (x + 3)² = 2y² + 15.
Transcribed Image Text:36 Equations of Order One [Ch. 2 - 2 24. (1 – xy)-2 dx + [y² + x²(1 – xy)-²] dy = 0; when x = 4, y = 1. ANS. хy* — уз + 3ху — 3х — 3 %3D 0. - 25. (ye* – 2y³) dx + (x e*" – 6xy² – 2y) dy = 0; when x = 0, y = 2. ANS. e*y = 2xy³ + y² – 3. = 0. = c + 2x(3 + y + y²). 26. (3 + y + 2y² sin² x) dx + (x + 2xy – y sin 2x) dy ANS. y? sin 2x 27. 2x[3x + у — у ехр (— х?)] dx + [x? + 3у? + еxp (-х?) dy 3D 0. ANS. x²y + y³ + 2x³ + y exp (–-x²) = c. | 28. (ху? + х — 2у + 3) dx + x^у dy 3D 2(х + у) dy; when x 3D 1, у %3D 1. ANS. (xy – 2)2 + (x + 3)² = 2y² + 15.
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