If $y = A \cos nx + B \sin nx$,then $\frac{d^2 y}{dx^2} = $

$y=e^{a \sin ^{-1} x} \Rightarrow (1-x^2) y_{n+2}-(2 n+1) x y_{n+1}$ is equal to

$f(x)$ is a twice differentiable function such that $f^{\prime \prime}(x)=-f(x)$ and $f^{\prime}(x)=g(x)$. If $h(x)=(f(x))^2+(g(x))^2$ and $h(1)=2$, then $h(2)=$

If $f(x)=x^3-x^2 f^{\prime}(1)+x f^{\prime \prime}(2)-f^{\prime \prime \prime}(3), x \in R$,then

$\frac{d^n}{dx^n}(e^{2x} + e^{-2x}) = $

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