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Question

Solution ofxsinyxdy=ysinyx-xdx is


A

cosyx=c

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B

logyx+logx=c

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C

logyx-logx=c

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D

None of these

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Solution

The correct option is D

None of these


Explanation for the correct answer:

Simplifying the given expression:

xsinyxdy=ysinyx-xdxsinyxdydx=yxsinyx-1...(1)

Substitute yx=v

cdydx-yx2=dvdxcdydx-y=x2dvdxFrom(1)1xx2dvdx+y·sinv=vsinv-1xdvdx·sinv=-1

Integrating on both the sides

dvsinv=dxxcosyx=logx+ccosyx+c=logx

Therefore, the correct answer is option (D).


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