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$The solution of the D.E [x coty + \log \cos x] d y + (logsiny-ytanx) d x = 0 is$

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a

sinxycosyx=C

b

sinyxcosxy=C

c

sinxxcosyy=C

d

tanxtany=C

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detailed solution

Correct option is B

[xcoty+log⁡cos⁡x]dy+( logsiny-ytanx )dx=0[xcoty+log⁡cos⁡x]dydx +( logsiny-ytanx )=0xcotydydx+logcosxdydx+log siny-ytanx=0xcotydydx+logsiny-ytanx+logcosxdydx=0∫d(xlogsiny)+∫d(ylogcos⁡x)=C→xlog⁡sin⁡y+ylog⁡cos⁡x=C→(sin⁡y)x(cos⁡x)y=C

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