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B. (y + e*seny)x + (x + e*cosy)dy = 0

B. (y + e*seny)x + (x + e*cosy)dy = 0

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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B. (y + e*seny)x + (x + e*cosy)dy = 0
Transcribed Image Text:B. (y + e*seny)x + (x + e*cosy)dy = 0
Expert Solution
Step 1

The differential equation is given as 

y+exsinydx+x+excosydy=0

Compare it with Mdx+Ndy=0 to obtain 

M=y+exsinyN=x+excosy

Consider

∂M∂y=∂∂yy+exsiny=1+excosy∂N∂x=∂∂xx+excosy=1+excosy

As ∂M∂y=∂N∂x , the given differential equation is exact.

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