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Question

If xdydx=y(log ylog x+1), then the solution of the equation is

A
y log(xy)=cx
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B
x log(yx)=cy
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C
log(yx)=cx
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D
log(xy)=cx
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Solution

The correct option is C log(yx)=cx
dydx=yx(logyx+1)
Put y=vxdydx=v+xdvdx
v+xdvdx=v log v+v1vlogvdv=1xdx1v log vdv=1xdxlog(log v)=logx+log c
logyx=cx

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