If $y=2 \cos (2 \log x)+3 \sin (2 \log x)$, then $x^2 y^{\prime \prime}+x y^{\prime}+2 y=$

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

Let $\cos ^{-1}\left(\frac{y}{b}\right)=\log \left(\frac{x}{n}\right)^{n}$. Then

$A$ function $y = f(x)$ has a second-order derivative $f''(x) = 6(x - 1)$. If its graph passes through the point $(2, 1)$ and at that point the tangent to the graph is $y = 3x - 5$,then the function is

If $f(x) = \sin(\sin x)$ and $f''(x) + \tan x f'(x) + g(x) = 0$,then $g(x)$ is

If $\sqrt{x+y}-\sqrt{x-y}=c$, then $\frac{d^2 y}{d x^2}=$