If y = x + frac{1}{x},then which among the fo | vedclass

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(C) Given that $y = x + \frac{1}{x}$.Differentiating with respect to $x$:$\frac{dy}{dx} = 1 - \frac{1}{x^2}$.This can be written as $y' = \frac{x^2 -

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$x^2 y' - x y + 2 = 0$

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(C) Given that $y = x + \frac{1}{x}$.Differentiating with respect to $x$:$\frac{dy}{dx} = 1 - \frac{1}{x^2}$.This can be written as $y' = \frac{x^2 - 1}{x^2}$.Multiplying both sides by $x^2$:$x^2 y' = x^2 - 1$.Rearranging the terms:$x^2 y' - x^2 + 1 = 0$.We know that $y = x + \frac{1}{x}$,so $x y = x(x + \frac{1}{x}) = x^2 + 1$.Substituting $x^2 = x y - 1$ into the equation $x^2 y' - x^2 + 1 = 0$:$x^2 y' - (x y - 1) + 1 = 0$.$x^2 y' - x y + 1 + 1 = 0$.$x^2 y' - x y + 2 = 0$.

If $y = x + \frac{1}{x}$,then which among the following holds?

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