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Question

If u=xyx2+y2, then xux+yuy=

A
u
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B
u
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C
3u
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D
0
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Solution

The correct option is D 0

u is homogeneous equation of degree n=0.
xdudx=nu
xdudx=0
Alternate solution,
dudx=x2+y2(ny)(x2+y2)xx2+y2
xdudx=xx2+y2(xy)x2x2+y2x2+y2
ydudy=yx2+y2(xy)y2x2+y2x2+y2
xdudx=(xy)x2+y2(xy)x2+y2x2+y2
=0


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