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Question

The general solution of the differential equation ydxxdy+lnxdx=0 is
(where C is constant of integration)

A
y+lnx+1=Cx
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B
ylnx1=C
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C
y+lnx1=Cx
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D
y+lnx1=C
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Solution

The correct option is A y+lnx+1=Cx
Given differential equation
ydxxdy+lnxdx=0
Dividing by x2, we get
xdyydxx2lnxx2dx=0
d(yx)lnxx2dx=0
Integrating both sides, we have
yxlnxx2dx=0
yx+1xlnx1x2dx=0
yx+1xlnx+1x=C
y+lnx+1=Cx

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