If `y=acos((log)_e x)+bsin((log)_e x)` , then `x^2\ y_2+x y_1=` (a) 0 (b) `y` (c) ` y` (d) none of these

Explanation

`y=a cos (log x)+b sin (log x)`
`
frac{d y}{d x}=frac{-a sin (log x)}{x}+frac{b sin (log x)}{x}`
`
x frac{d y}{d x}=-a sin (log x)+b sin (log x) `
`
x frac{d^{2} y}{d x^{2}}+frac{d y}{d x}=frac{-a cos (log x)}{x}-frac{b sin (log x)}{x}`
`
x^{2} frac{d^{2} y}{d x^{2}}+x frac{d y}{d x}=-a cos (log x)-b sin (log x) `
`
x^{2} frac{d^{2} y}{d x^{2}}+x frac{d y}{d x}=-y`
`
x^{2} frac{d^{2} y}{d x^{2}}+x frac{d y}{d x}+y=0`