$$frac{dy}{dx} =frac{-1}{mcos^{-1} x (sqrt{1-x^2})}$$

$$frac{dy}{dx} = -frac{1}{(e^y)sqrt{1-x^2}}$$

So

$$frac{d^2y}{dx^2} = (frac{1}{(e^{2y})(1-x^2)})(frac{-e^yx}{sqrt{1-x^2}}+e^y sqrt{1-x^2} frac{dy}{dx})$$

I am not able to rearrange this into the required from. How should I proceed?