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

Let $\bar{A}, \bar{B}, \bar{C}$ be vectors of lengths 3 units, 4 units, 5 units respectively. let $\bar{A}$ be perpendicular to $\overline{\mathrm{B}}+\overline{\mathrm{C}}, \overline{\mathrm{B}}$ be perpendicular to $\overline{\mathrm{C}}+\overline{\mathrm{A}}$ and $\overline{\mathrm{C}}$ be perpendicular to $\bar{A}+\bar{B}$, then the length of vector $\overline{\mathrm{A}}+\overline{\mathrm{B}}+\overline{\mathrm{C}}$ is

The approximate value of $x^3-2 x^2+3 x+2$ at $x=2.01$ is

The general solution of $\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{x+y+1}{x+y-1}$ is