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Question

The solution of the differential equation [y(1+x-1)+siny]dx+[x+logx+xcosy]dy=0 is


A

xy+ylogx=c

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B

xy+xsiny=c

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C

xy+ylogx+xsiny=c

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D

None of these

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Solution

The correct option is C

xy+ylogx+xsiny=c


The explanation for the correct answer.

Find the solution to the equation:

Given: [y(1+x-1)+siny]dx+[x+logx+xcosy]dy=0

Expand the given equation

y+yx+sinydx+x+logx+xcosydy=0ydx+yxdx+sinydx+xdy+logxdy+xcosydy=0ydx+xdy+yxdx+logxdy+sinydx+xcosydy=0ydx+xdy=d(xy),yxdx+logxdy=dylogx,sinydx+xcosydy=dxsinyd(xy)+dylogx+dxsiny=0

Integrate the above equation

xy+ylogx+xsiny=C

Hence option C is the correct answer.


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