Let $y=y\left(x\right)$ satisfies the equation $\frac{dy}{dx}-\left|A\right|=0,$ for all $x>0,$ where $A=\left[\begin{array}{ccc}y& \sin x& 1\\ 0& -1& 1\\ 2& 0& \frac{1}{x}\end{array}\right]$. If $y\left(\pi \right)=\pi +2,$ then the value of $y\left(\frac{\pi }{2}\right)$ is:

Let $y=y\left(x\right)$ be solution of the following differential equation 

$e^y\frac{dy}{dx}-2e^y\sin x+\sin x{\cos }^{2}x=0, y\left(\frac{\pi }{2}\right)=0$.

If $y\left(0\right)={\log }_{\mathrm{e}}\left(\alpha +\beta {\mathrm{e}}^{-2}\right)$, then $4(\alpha +\beta )$ is equal to            .