If $\cos ^{-1}\left(\frac{y}{b}\right)=2 \log \left(\frac{x}{2}\right)$,where $x>0$,then $x^2 \frac{d^2 y}{d x^2}+x \frac{d y}{d x}$ is equal to

If the three functions $f(x)$,$g(x)$,and $h(x)$ are such that $h(x) = f(x) \cdot g(x)$ and $f^{\prime}(x) \cdot g^{\prime}(x) = c$,where $c$ is a constant,then $\frac{f^{\prime \prime}(x)}{f(x)} + \frac{g^{\prime \prime}(x)}{g(x)} + \frac{2c}{f(x) \cdot g(x)}$ is equal to:

If $y=a \cos (\log x)+b \sin (\log x)$,then $x^2 y_2+x y_1=$

If $\sqrt{x+y}-\sqrt{x-y}=c$, then $\frac{d^2 y}{d x^2}=$

If $(a+bx) e^{\frac{y}{x}}=x$,then $x^3 \frac{d^2 y}{d x^2}$ is equal to

If $y = \cos^{-1} x$,find $\frac{d^{2} y}{d x^{2}}$ in terms of $y$ alone.