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If y = a cos ⁡ ( log ⁡ x ) + b sin ⁡ ( log ⁡ x ) , where a   &   b are parameters, then x 2 y " + x y ' is equal to

Options

  1. Ay
  2. B- y
  3. C2 y
  4. D- 2 y

Correct answer

B. - y

Step-by-step solution

y = a cos ⁡ ( log ⁡ x ) + b sin ⁡ ( log ⁡ x ) On differentiating w.r.t. x , we get y ′ = − a sin ( log x ) x + b cos ( log x ) x ⇒ x y ′ = − a sin ( log x ) + b cos ( log x ) Again, on differentiating w.r.t. x , we get x y ″ + y ′ = − a cos ( log x ) 1 x − b sin ( log x ) 1 x ⇒ x 2 y ″ + y ′ x = − a cos ( log x ) + b sin ( log x ] ⇒ x 2 y ″ + x y ′ = − y

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