Show that an implicit solution of 2x sin²(y) dx - (+² +17) cos(y) dy = 0 is given by In(x² +17) + csc(y) = C. Differentiating In(x² + 17) + csc(y) = C we get y = CSc 2x x² + 17 X cos (y) sin² (y) dy dx = 0 or 2x sin²(y) dx + Find the constant solutions, if any, that were lost in the solution of the differential equation. (Let k represent an arbitrary integer.) c−¹(k − ln(x² +17)) - (x² +17) cos(y) )dy = 0.
Show that an implicit solution of 2x sin²(y) dx - (+² +17) cos(y) dy = 0 is given by In(x² +17) + csc(y) = C. Differentiating In(x² + 17) + csc(y) = C we get y = CSc 2x x² + 17 X cos (y) sin² (y) dy dx = 0 or 2x sin²(y) dx + Find the constant solutions, if any, that were lost in the solution of the differential equation. (Let k represent an arbitrary integer.) c−¹(k − ln(x² +17)) - (x² +17) cos(y) )dy = 0.
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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Transcribed Image Text:Show that an implicit solution of
2x sin²(y) dx - (x² + 17) cos(y) dy = 0
is given by In(x² +17) + csc(y) = C.
Differentiating In(x² + 17) + csc(y) = C we get
y = csc
2x
x² + 17
X
cos (y)
sin ² (y)
dy
dx
= 0 or 2x sin²(y) dx + - (x² +17)
Find the constant solutions, if any, that were lost in the solution of the differential equation. (Let k represent an arbitrary integer.)
;−¹(k − ln(x² +17))
-17) cos(y)
Jay - U.
0.
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