If $y = 1 - x + \frac{x^2}{2!} - \frac{x^3}{3!} + \frac{x^4}{4!} - \dots$,then $\frac{d^2y}{dx^2} = $

If $f(x) = b e^{ax} + a e^{bx}$,then $f^{\prime \prime}(0)$ is equal to

If $y=a \sin x+(5+2 x) \cos x$,then $y^{\prime \prime}+y=$

If $y=\tan \left(3 \tan ^{-1} x\right)$,then $\left(1-3 x^2\right) \frac{d^2 y}{d x^2}-12 x \frac{d y}{d x}=$

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