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Question
If `"u"(x , y) = (x^2 + y^2)/sqrt(x + y)`, prove that `x (del"v")/(delx) + y (del"u")/(dely) = 3/2 "u"`
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Solution
`"u"(x , y) = (x^2 + y^2)/sqrt(x + y)`
`"u"(lambdax , lambday) = (lambda^2x^2 + lambda^2y^2)/sqrt(lambdax + lambday)`
= `(lambda^2(x^2 + y^2))/(lambda^(1/2) sqrt(x + y))`
= `(lambda^(1/2) (x^2 + y^2))/sqrt(x + y)`
u is a homogeneous function of degree `3/2`
By Euler's Theorem,
`x (del"v")/(delx) + y (del"u")/(dely) = 3/2 "u"`
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