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

Variables $x$ and $y$ are related by the equation $x = \int\limits_0^y \frac{dt}{\sqrt{1 + t^2}}$. The value of $\frac{d^2y}{dx^2}$ is equal to

If $y=\frac{\log _e x}{x}$ and $z=\log _e x$,then $\frac{d^2 y}{d z^2}+\frac{d y}{d z}$ is equal to

If $y=f(x)$ is a twice differentiable function such that at a point $P$,$\frac{dy}{dx}=4$ and $\frac{d^2y}{dx^2}=-3$,then $\left(\frac{d^2x}{dy^2}\right)_P$ is equal to:

If $(a+b x) e^{\frac{y}{x}}=x$,then $\frac{d^2 y}{d x^2}=$

$\frac{d^2}{dx^2}(2\cos x \cos 3x) = $