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.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 36CR
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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.
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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ISBN:
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