Verify that `y=e^(m cos^-1 x)` satisfies the differential equation `(1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-m^2y=0`

Explanation

We :

` y=e^{m cos ^{-1} x}...(i)`


Differentiating (i), with respect to x, we obtain

`
frac{d y}{d x}=e^{m cos ^{-1} x} cdot m(frac{-1}{sqrt{1-x^{2}}})`

`

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

`
Rightarrow(1-x^{2})(frac{d y}{d x})^{2}=m^{2} y^{2}`



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