Question

If y =sin (log x), then `x^2 ("d"^2"y")/"dx"^2 + x "dy"/"dx" + "y"` is equal to ______.

Options

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Answer 1

If y =sin (log x), then `x^2 ("d"^2"y")/"dx"^2 + x "dy"/"dx" + "y"` is equal to 0.

Explanation:

y = sin (log x)     ...(i)

`therefore "dy"/"dx" = cos (log x) * 1/x`

`=> x "dy"/"dx" = cos (log x)`

Differentiating both sides w.r.t. x, we get

`x ("d"^2"y")/"dx"^2 + "dy"/"dx" * 1 = - sin (log x) * 1/x`

`=> "x"^2 ("d"^2"y")/"dx"^2 + x "dy"/"dx"` = - y    ....[From (i)]

`=> "x"^2 ("d"^2"y")/"dx"^2 + x "dy"/"dx"`+ y = 0