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If y=(1/2)^(n-1)cos(ncos^(-1)x), then pr...

If `y=(1/2)^(n-1)cos(ncos^(-1)x),` then prove that `y` satisfies the differential equation `(1-x^2)` `(d^2y)/(dx^2)-x(dy)/(dx)+n^2y=0`

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