For $y=7 \sin x+5 \cos x$,if $\frac{d^2 y}{d x^2}-m y=0$,then $m=$ . . . . . .

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:

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

If $f(x)=\frac{x-1}{e^x}$, then $f^{\prime}(0)+f^{\prime \prime}(0)=$

$\begin{aligned} & y=\sin \left(\log \left(x^2+2 x+1\right)\right) \\ & \Rightarrow(x+1)^2 \frac{d^2 y}{d x^2}+(x+1) \frac{d y}{d x}= \end{aligned}$

If $2x = y^{1/5} + y^{-1/5}$ and $(x^2 - 1) \frac{d^2y}{dx^2} + \lambda x \frac{dy}{dx} + ky = 0$,then $\lambda + k$ is equal to