If \( \mathrm{y}=\mathrm{x}+\frac{1}{\mathrm{x}} \), then (1) \( x^...

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If \( \mathrm{y}=\mathrm{x}+\frac{1}{\mathrm{x}} \), then
(1) \( x^{2} \frac{d y}{d x}+x y=0 \)
(2) \( x^{2} \frac{d y}{d x}+x y+2=0 \)
(3) \( x^{2} \frac{d y}{d x}-x y+2=0 \)
(4) \( x \frac{d y}{d x}-x y=0 \)
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