If `y=cosec^(-1)x ,\ \ x >1` , then show that `x(x^2-1)(d^2y)/(dx^2)+(2x^2-1)(dy)/(dx)=0` .

Explanation

Consider
`y=cosec^{-1} x`

Differentiating both sides w.r.t. x
`

frac{d y}{d x}=frac{-1}{x sqrt{x^{2}-1}} `
`Rightarrow quad x sqrt{x^{2}-1} frac{d y}{d x}=-1`


Again differentiating w.r.t. x, we get


`x sqrt{x^{2}-1} cdot frac{d^{2} y}{d x^{2}}+sqrt{x^{2}-1} frac{d y}{d x}+x frac{2 x}{2 sqrt{x^{2}-1}} frac{d y}{d x}=0 `
`
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