[EAMCET 2001]
A) $ xu _{x}=yy _{y} $
B) $ yu _{x}=xu _{y} $
C) $ yu _{x}+xu _{y}=0 $
D) $ x^{2}u _{y}+y^{2}u _{x}=0 $
Correct Answer: B
$ u _{x}={e^{-x^{2}-y^{2}}}(-2x)=-2ux $ , $ u _{y}={e^{-x^{2}-y^{2}}}(-2y)=-2uy $
$ yu _{x}=xu _{y} $ .
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