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35. x dx + Ja? - x² dy = 0. ,2

35. x dx + Ja? - x² dy = 0. ,2

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 answer item no. 35 and show your detailed solution..
26 Equations of Order One 25. (1- y)y' x?. 26. x'yy e. 27. tan? y dy = sin x dx. 28. y' 29. y' = y sec x. 30. dx = t(1 + 12) sec? x dt. 31. (e2x + 4)y' = y. 32. a dB + B da + aß(3 da + dß) = 0. 33. (1+ In x) dx + (1+ In y) dy = 0. 34. x dx – Ja? - x² dy = 0. = cos x cos y. 35. x dx + Ja? – x² dy = 0. 36. a? dx = x/x? - a² dy. 37. y In x In y dx + dy = 0. 8. Homogeneous Functions Polynomials in which all terms are of the same degree, such as x2 - 3xy + 4y2, x' + y', x*y + 7y°, (1) are called homogeneous polynomials. We wish now to extend the homogeneity so it will apply to functions other than polynomials. If we assign a physical dimension, say length, to each variable x and v in the polynomials in (1), then ecach polynomial itself also has a dimension, length to some power. This suggests the desired generalization. concept of physical
Transcribed Image Text:26 Equations of Order One 25. (1- y)y' x?. 26. x'yy e. 27. tan? y dy = sin x dx. 28. y' 29. y' = y sec x. 30. dx = t(1 + 12) sec? x dt. 31. (e2x + 4)y' = y. 32. a dB + B da + aß(3 da + dß) = 0. 33. (1+ In x) dx + (1+ In y) dy = 0. 34. x dx – Ja? - x² dy = 0. = cos x cos y. 35. x dx + Ja? – x² dy = 0. 36. a? dx = x/x? - a² dy. 37. y In x In y dx + dy = 0. 8. Homogeneous Functions Polynomials in which all terms are of the same degree, such as x2 - 3xy + 4y2, x' + y', x*y + 7y°, (1) are called homogeneous polynomials. We wish now to extend the homogeneity so it will apply to functions other than polynomials. If we assign a physical dimension, say length, to each variable x and v in the polynomials in (1), then ecach polynomial itself also has a dimension, length to some power. This suggests the desired generalization. concept of physical
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