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Question

The slope of a curve at any point (x,y) other than the origin, is y+yx. Then, the equation of the curve is

A
y=Cxex
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B
y=x(ex+C)
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C
xy=Cex
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D
y+xex=C
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E
(yx)ex=C
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Solution

The correct option is C y+xex=C
Slope of a curve at (x,y) is given by dydx.
According to the equation,
dydx=y+yx
dydx=y(1+1x)
dyy=(1+1x)dx
logy=x+logx+logC
logy=log(Cxex) [x=logex]
y=Cxex

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