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Show that an implicit solution of 2x sin²(y) dx - (x² + 18) cos(y) dy = 0 is given by In(x² + 18) + csc(y) = C. Differentiating In(x² + 18) + csc(y) = C we get 2x

Show that an implicit solution of 2x sin²(y) dx - (x² + 18) cos(y) dy = 0 is given by In(x² + 18) + csc(y) = C. Differentiating In(x² + 18) + csc(y) = C we get 2x

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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Show that an implicit solution of is given by In(x² + 18) + csc(y) = C. 2x sin²(y) dx - (x² + 18) cos(y) dy = 0 Differentiating In (x² + 18) + csc(y) = C we get y = kn + 2x x² + 18 X Find the constant solutions, if any, that were lost in the solution of the differential equation. (Let k represent an arbitrary integer.) π 2 X -cos(y) sin (²) Your answer cannot be understood or graded. More Information dy dx = 0 or 2x sin²(y) dx + |(−cos (y)) (x² +10) dy = 0. X
Transcribed Image Text:Show that an implicit solution of is given by In(x² + 18) + csc(y) = C. 2x sin²(y) dx - (x² + 18) cos(y) dy = 0 Differentiating In (x² + 18) + csc(y) = C we get y = kn + 2x x² + 18 X Find the constant solutions, if any, that were lost in the solution of the differential equation. (Let k represent an arbitrary integer.) π 2 X -cos(y) sin (²) Your answer cannot be understood or graded. More Information dy dx = 0 or 2x sin²(y) dx + |(−cos (y)) (x² +10) dy = 0. X
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