If `y = sin (In x)`, then which one of thefollowing is correct?

Options

A. `(d^(2)y)/(dx^(2))+y=0`
B. ` (d^(2)y)/(dx^(2))=0`
C. ` x^(2) (d^(2)y)/(dx^(2)) + x (dy)/(dx) +y=0`
D. ` x^(2) (d^(2)y)/(dx^(2)) -x (dy)/(dx) +y=0`

Answer

C

Explanation

` y= sin (log x)`
` Rightarrow (dy)/(dx) = (cos(logx))/x`
`Rightarrow x ((dy)/(dx))= cos(logx)`
Again differentiating
` x(d^(2)y)/(dx^(2)) + (dy)/(dx) = - (sin log x)/(x) = (-y)/x`
` Rightarrow x^(2) (d^(2)y)/(dx^(2))+ x (dy)/(dx) +y=0`