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Question

If u=3y3xx+y then xux+yuy=?

A
23u
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B
23u
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C
32u
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D
32u
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Solution

The correct option is B 23u

u is a homogeneous eqn of degree n=23


xux=nu


xux=23u


Alternate method

ux=13x2/3(x+y)((y)1/3x1/3)(x+y)2

xux=13x1/3(x+y)x(y1/3x1/3)(x+y)2

yuy=13y1/3(x+y)y(y1/3x1/3)(x+y)2

xux=13(y1/3x1/3)(x+y)(x+y)(y1/3x1/3)(x+y)2

=(131)u=23u


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