If $y=2 \sin x+3 \cos x$ and $y+A \frac{d^2 y}{d x^2}=B$,then the values of $A$ and $B$ are respectively:

If $y = (\sin^{-1} 2x)^2 + (\cos^{-1} 2x)^2$, then $(1 - 4x^2) y_2 - 4x y_1 = $

If $y=\tan ^{-1}\left[\frac{\log _e\left(\frac{e}{x^2}\right)}{\log _e\left(e x^2\right)}\right]+\tan ^{-1}\left[\frac{3+2 \log _e x}{1-6 \log _e x}\right]$, then $\frac{d^2 y}{d x^2}=$

If $y=\log \left(x-\sqrt{x^2-1}\right)$, then $\left(x^2-1\right) y^{\prime \prime}+x y^{\prime}$ is equal to:

Find the second-order derivative of the function $f(x) = x^{3} \log x$.

If $y = {\left[ {x + \sqrt {{x^2} - 1} } \right]^{15}} + {\left[ {x - \sqrt {{x^2} - 1} } \right]^{15}}$,then $\left( {{x^2} - 1} \right)\frac{{{d^2}y}}{{d{x^2}}} + x\frac{{dy}}{{dx}}$ is equal to