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Question

The solution of the differential equation ydxxdy+logxdx=0 is

A
y=logx+cx
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B
y=1+logx+c
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C
y+cx=log1x
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D
None of these
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Solution

The correct option is A None of these
Given differential equation

ydxxdy+logxdx=0

Here, M=y+logx , N=x

δMδy=1

δNδx=1

δMδyδNδx
Given differential eqn is not exact.

To make it exact, multiply given differential eqn by 1x2

ydxxdyx2+logxx2dx=0

xdyydxx2logxx2dx=0

d(yx)logxx2dx=0

Integrating , we get

yxlogxx2dx=0

yx+1xlogx1x1xdx=c

yx+logxx+1x=c

y+logx+1=cx

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