If y = x + 1 x , then which among the following holds?

Question

If y = x + 1 x , then which among the following holds?, x 2 y ' + x y = 0, x 2 y ' + x y + 2 = 0, x 2 y ' − x y + 2 = 0, x 2 y ' + x y − 2 = 0

MARKS App · Accepted Answer

Given that y = x + 1 x Differentiate with respect to x d y d x = 1 - 1 x 2 ⇒ y ' = x 2 - 1 x 2 ⇒ x 2 y ' = x 2 - 1 ⇒ x 2 y ' - x 2 + 1 = 0 ⇒ x 2 y ' - x x - 1 x = 0 ⇒ x 2 y ' - x x + 1 x + 2 = 0 ⇒ x 2 y ' - x y + 2 = 0

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