If $y=x \log \left(\frac{1}{a x}+\frac{1}{a}\right)$,then $x(x+1) \frac{d^2 y}{d x^2}+x \frac{d y}{d x}-y=$

If $y^2 = ax^2 + bx + c$,where $a, b, c$ are constants,then $y^3 \frac{d^2 y}{dx^2}$ is equal to

If $y = e^{\tan^{-1}x}$,then $(1 + x^2)\frac{d^2y}{dx^2} = $

If $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$,then $\frac{d^2 y}{d x^2}=$

If $f: R \rightarrow R$ is an even function which is twice differentiable on $R$ and $f^{\prime \prime}(\pi)=1$,then $f^{\prime \prime}(-\pi)$ is equal to

If $y^{1/4} + y^{-1/4} = 2x$,and $(x^2 - 1) \frac{d^2y}{dx^2} + \alpha x \frac{dy}{dx} + \beta y = 0$,then $|\alpha - \beta|$ is equal to ...... .