# If \$y=log (m cos^{-1} x)\$ is a solution of the equation \$(1-x^2)frac{d^2y}{dx^2}-xfrac{dy}{dx}=ke^{-2y}\$

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

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?