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B. Homogeneous 1. у(x*+ ху - 2у') dx + x(Зу? — ху —х?) dy 3D 0 2. (x+y sin 2) dx-x sin dy 0 3. xy dx + 2(x² + 2y?) dy 0; x = 0, y = 1 4. y(x? + y) dx + x(3x?- 5y) dy = 0; x =2, 2ys-2y'x? + 3x = 0 y = C sin Y = x sin (C- In x) In x+ cos ? = C %3D y=1 5. xy' y-x2 - y? 2y In+ 2xy + x² = Cy y(3x? + 4y?) = 4 |

B. Homogeneous 1. у(x*+ ху - 2у') dx + x(Зу? — ху —х?) dy 3D 0 2. (x+y sin 2) dx-x sin dy 0 3. xy dx + 2(x² + 2y?) dy 0; x = 0, y = 1 4. y(x? + y) dx + x(3x?- 5y) dy = 0; x =2, 2ys-2y'x? + 3x = 0 y = C sin Y = x sin (C- In x) In x+ cos ? = C %3D y=1 5. xy' y-x2 - y? 2y In+ 2xy + x² = Cy y(3x? + 4y?) = 4 |

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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Kindly solve items 4 and 5. Show the complete solution. Again, items 4 and 5 only.
B. Homogeneous 1. у(x*+ ху - 2у) dx + x(3у? - ху — х') dy 3D0 2. (x + y sin 2) dx - x sin 2 dy = 0 3. xy dx + 2(x? + 2y?) dy = 0; x = 0, y = 1 4. y(x2 + y) dx + x(3x²-5y) dy = 0; x =2, 2y-2y'x? + 3x = 0 y = C sin Y = x sin (C- In x) In x + cos = c y=1 y3 2y? In+ 2xy + x² = Cy y'(3x? + 4y?) = 4 5. xy' = y- Vx2 - y?
Transcribed Image Text:B. Homogeneous 1. у(x*+ ху - 2у) dx + x(3у? - ху — х') dy 3D0 2. (x + y sin 2) dx - x sin 2 dy = 0 3. xy dx + 2(x? + 2y?) dy = 0; x = 0, y = 1 4. y(x2 + y) dx + x(3x²-5y) dy = 0; x =2, 2y-2y'x? + 3x = 0 y = C sin Y = x sin (C- In x) In x + cos = c y=1 y3 2y? In+ 2xy + x² = Cy y'(3x? + 4y?) = 4 5. xy' = y- Vx2 - y?
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