If `y=a[x+(x^2-1)^(1/2)]^n+b[x-(x^2-1)^(1/2)]^n` the value of the expression `(x^2-1)(d^2y) / dx^2+x dy / dx-n^2y` is __________.

Explanation

Let,


`p=x+(x^2-1)^(1/2)`


`(dp)/(dx)=1+(2x)/(2sqrt(x^2-1))`


`(dp)/(dx)=(x+(x^2-1)^(1/2))/(sqrt(x^2-1))`


`(dp)/(dx)=(p)/(sqrt(x^2-1))`


`y=ap^n+bp^(-n)`


`(dy)/(dx)=anp^(n-1)(dp)/(dx)-bnp^(-n-1)(dp)/(dx)`


`(dy)/(dx)=(anp^(n)-bnp^(-n))/(sqrt(x^2-1))`


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