If y=e^(acos^(-1)x), -1lt=xlt=1,show tha...

If `y=e^(acos^(-1)x), -1lt=xlt=1,`show that `(1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-a^2y=0`.

AI Generated Solution

To solve the problem, we need to show that: \[ (1 - x^2) \frac{d^2y}{dx^2} - x \frac{dy}{dx} - a^2 y = 0 \] where \( y = e^{a \cos^{-1}(x)} \). ...

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