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If $u=f\large\left(\frac {y}{x} \right) $ then $x\large\frac{\partial u}{\partial x}$+$y\large\frac{\partial u}{\partial y}$ is equal to

\[\begin{array}{1 1}(1)0&(2)1\\(3)2u&(4)u\end{array}\]

1 Answer

$u=f( \large\frac{y}{x})$
u is a homogeneous function of degree 0
Euler's theorem,
$ x \large\frac{\partial u}{\partial x} $$+ y \large\frac{\partial u}{\partial y}$$=0.f$
$ x \large\frac{\partial u}{\partial x} $$+ y \large\frac{\partial u}{\partial y}$$=0$
Hence 1 is the correct answer.
answered May 20, 2014 by meena.p
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